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Current Electricity - Chapter Outline
Lesson 1: Electric Current
What is an Electric Circuit?
Requirements of a Circuit
Electric Current
Lesson 2: Electrical Resistance
Journey of a Typical Electron
Resistance
Lesson 3: Ohm’s Law
Ohm's Law
Lesson 4: Electrical Power
Power: Putting Charges to Work
Common Misconceptions Regarding Electric Circuits
Lesson 3: Circuit Connections
Circuit Symbols and Circuit Diagrams
Two Types of Connections
Series Circuits
Parallel Circuits
Lesson 1: Electric Current objectives
1.
2.
3.
4.
5.
What is an Electric Circuit?
Requirements of a Circuit
Electric Current
Power: Putting Charges to Work
Common Misconceptions Regarding Electric
Circuits
What is an Electric Circuit?
A circuit is simply a closed loop through which
charges can continuously move.
lab: light a light bulb
• you are given the following material, what arrangement
would result in the successful lighting of the bulb?
• Record all different ways your connection did not work.
• Record all different ways your connection did work.
• Write your conclusion – what you must do in order for the
light bulb to work.
Light Bulb Anatomy
• A light bulb is a device consisting of a
filament attached to two wires. The
wires and the filament are conducting
materials which allow charge to flow
through them. One wire is connected
to the ribbed sides of the light bulbs.
The other wire is connected to the
bottom base of the light bulb. The
ribbed edge and the bottom base are
separated by an insulating material
which prevents the direct flow of
charge between the bottom base and
the ribbed edge. The only pathway by
which charge can make it from the
ribbed edge to the bottom base or
vice versa is the pathway which
includes the wires and the filament.
+
• The successful means of lighting the bulb involves
placing the bottom base of the bulb on one terminal
and connecting the ribbed edge to the other terminal
using a wire.
The Requirement of a circuit
1. There must be a closed conducting loop in the external
circuit which stretches from the high potential, positive
terminal to the low potential, negative terminal.
2. There must be an energy supply capable doing work
on charge to move it from a low energy location to a
high energy location and thus establish an electric
potential difference across the two ends of the external
circuit.
example
1. As a + charge moves through the battery from D to A, it
(gains, loses) potential energy and (gains, loses) electric
potential. The point of highest energy within a battery is
the (+, -) terminal.
2. As a + charge moves through the external circuit from A
to D, it (gains, loses) potential energy and (gains, loses)
electric potential. The point of highest energy within the
external circuit is closest to the (+, -) terminal.
3. Use >, <, and = signs to compare the electric potential
(V) at the four points of the circuit.
VA ____ VB_______ VC _________VD
Electric Current
• If the two requirements of an electric circuit are met, then
charge will flow through the external circuit. This flow of
charge or current, is the rate at which charge flows past a
point on a circuit.
Current is a rate quantity. Like velocity - the rate at which an
object changes its position. Acceleration - the rate at which
an object changes its velocity. And power - the rate at which
work is done on an object. In every case of a rate quantity,
the mathematical equation involves some quantity over time.
• Electric current refers to the rate at which charge passes
a given point in a circuit.
q
current : I 
t
Q: the amount of charge that passes a point, in Coulomb
t: time, in seconds
I, electric current, in ampere (A), which is a fundamental
unit.
1A=1C/s
Current can only be sustained if there is
difference in ELECTRICAL POTENTIAL or
VOLTAGE between two points!
• André-Marie Ampère (20
January 1775 – 10 June
1836) was a French physicist
and mathematician who is
generally regarded as one of
the main discoverers of
electromagnetism. The SI
unit of measurement of
electric current, the ampere,
is named after him.
Conventional Current Direction
The direction of an
electric current is by
convention the
direction in which a
positive charge
would move.
Current versus Drift Speed
Q
I
t
Current has to do with the number of coulombs of
charge that pass a point in the circuit per unit of
time.
• Drift speed refers to the average
distance traveled by a charge carrier per
unit of time.
Even though the drift speed is extremely
slow, the current could be big. This is
because there are many, many charge
carriers moving at once throughout the
whole length of the circuit.
The Nature of Charge Flow
• We know that the average drift speed of an electron is
very, very slow, why does the light in a room or in a
flashlight light immediately after the switched is turned on?
• Charge carriers in the wires of electric circuits are
electrons. They are already there supplied by the atoms of
the wire. Once the switch is turned to on, there is an
electric potential difference established across the two
ends of the external circuit. The electrons begin moving
along a zigzag path in their usual direction. Thus, the
flipping of the switch causes an immediate response
throughout every part of the circuit, setting charge carriers
everywhere in motion in the same net direction.
• While the actual motion of charge carriers occurs with a
slow speed, the signal that informs them to start moving
travels at a fraction of the speed of light.
• The charge carriers never become
consumed or used up. While the energy
possessed by the charge may be used up,
the charge carriers themselves do not
disintegrate, disappear or otherwise
become removed from the circuit. And
there is no place in the circuit where
charge carriers begin to pile up or
accumulate. The rate at which charge
enters the external circuit on one end is
the same as the rate at which charge
exits the external circuit on the other end.
Check Your Understanding
1.
A current is said to exist whenever _____.
a. a wire is charged
b. a battery is present
c. electric charges are unbalanced
d. electric charges move in a loop
2.
Current has a direction. By convention, current is in the direction that
___.
a. + charges move
b. - electrons move
c. + electrons move
3.
The drift velocity of mobile charge carriers in electric circuits is ____.
a. very fast; less than but very close to the speed of light
b. fast; faster than the fastest car but nowhere near the speed of light
c. slow; slower than Chris Rock runs the 200-meters
d. very slow; slower than a snail
4.
a.
b.
c.
d.
e.
f.
Use the diagram to complete the following statements:
A current of one ampere is a flow of charge at the rate of
_______ coulomb per second.
When a charge of 8 C flows past any point along a circuit in 2
seconds, the current is ________ A.
If 5 C of charge flow past point A (diagram at right) in 10
seconds, then the current is _________ A.
If the current at point D is 2.0 A, then _______ C of charge
flow past point D in 10 seconds.
If 12 C of charge flow past point A in 3 seconds, then 8 C of
charge will flow past point E in ________ seconds.
True or False: The current at point E is considerably less than
the current at point A since charge is being used up in the light
bulbs.
example
• If charge flowing at the rate of 2.50 × 1016 elementary
charges per second. What is the electric current?
q
I
t
Lesson 2: Electrical Resistance
1. Journey of a Typical Electron
2. Resistance
Resistance
• Resistance is the hindrance to the flow of charge. For an
electron, the journey from terminal to terminal is not a
direct route. Rather, it is a zigzag path which results from
countless collisions with fixed atoms within the
conducting material.
• While the electric potential difference established
between the two terminals encourages the movement
of charge, it is resistance which discourages it.
• The rate at which charge flows (current) from terminal to
terminal is the result of the combined affect of these two
quantities: potential difference and resistance.
Variables Affecting Electrical Resistance - R
1.
2.
3.
4.
The total length of the wires will affect the amount of resistance. The
longer the wire, the more resistance that there will be – R is directly
proportional to length.
The cross-sectional area of the wires will affect the amount of
resistance. The wider the wire, the less resistance that there will be to
the flow of electric charge – R is inversely proportional to Area.
The material that a wire is made of. Some materials are better
conductors than others and offer less resistance to the flow of charge.
Silver is one of the best conductors but is never used in wires of
household circuits due to its cost. Copper and aluminum are among
the least expensive materials with suitable conducting ability to
permit their use in wires of household circuits. The conducting
ability of a material is resistivity.
The temperature. Since resistity increases with increasing
temperature, the higher the temperature, the more resistance that
there will be. You can find a list of resistivity values for various
materials at temperatures of 20 degrees Celsius in your reference
table.
Mathematical Nature of Resistance
• The standard metric unit for resistance is the ohm,
represented by the Greek letter omega - Ω . The
equation representing the dependency of the resistance
(R) of a cylindrically shaped conductor (e.g., a wire) upon
the variables which affect it is:
L represents the length of the wire (in meters),
A represents the cross-sectional area of the wire (in m2),
ρ represents the resistivity of the material (in Ω•meter).
R represents the resistance of the wire (in Ω)
Graph of R vs. L and R vs. A
• If the length of the wire is increased, Resistance
is increased – direct linear relationship.
Linear
R
L
• If the area of the wire is increased, Resistance is
decreased – inverse relationship
Non Linear
R
A
example
•
An incandescent light bulb is supplied with a
constant potential difference of 120 volts. As
the filament of the bulb heats up,
1. What happens to the resistance?
2. What happens to the current?
example
• Determine the resistance of a 4.00 meter length of
copper wire having a diameter of 2.00 mm. Assume a
temperature of 20oC.
example
•What is the composition of a wire with a
• What isofthe
composition
of 5a xwire
a
resistance
31.8
Ohms if it is
107 with
meters
resistance
31.8 Ohms if area
it is 5ofx0.025
107 m2?
long
and has aofcross-sectional
meters long and has a cross-sectional area of
0.025 m2?
example
•
1.
2.
3.
4.
If the cross-sectional area of a metallic
conductor is halved and the length of the
conductor is doubled, the resistance of
the conductor will be ______________.
halved
doubled
unchanged
quadrupled
example
•
A 12.0-meter length of copper wire has a
resistance of 1.50 ohms. How long must an
aluminum wire with the same cross-sectional
area be to have the same resistance?
example
• Pieces of aluminum, copper, gold, and
silver wire each have the same length and
the same cross-sectional area. Which wire
has the lowest resistance at 20°C?
Lesson 3: Ohm’s law
• Ohm’s Law states the relationship between
current, potential difference and resistance. “At
constant temperature, the current in a metallic
conductor is directly proportional to the
potential difference between its ends, and
inversely proportional to its resistance.”
• Ohm’s Law is specific for certain materials and not
general law of electricity.
Ohm's Law: I = V / R
• Where:
V = potential in volts
I = current in amperes
R = resistance measured in ohms
V = R∙I
V
R=V/I
R
I
I=V/R
Resistance: R = V / I
• Since R = V / I, we say that the resistance, R, is the
constant of proportionality in Ohm’s law.
• Resistance = ∆v / ∆I, which is the slope of a potential
difference vs. current graph. The resistance is a
constant for a metallic conductor at constant
temperature.
V
V
Slope is resistance
I
I
Does not obey Ohm’s
Law
Ohm's Law as a Predictor of Current
V
I
R
• This equation indicates how the two variables (potential
difference and resistance) would affect the amount of current
in a circuit.
• The current in a circuit is directly proportional to the electric
potential difference impressed across its ends and inversely
proportional to the total resistance offered by the external
circuit.
• The greater the battery voltage (i.e., electric potential
difference), the greater the current. a twofold increase in the
battery voltage would lead to a twofold increase in the current
(if all other factors are kept equal).
• The greater the resistance, the less the current. An increase in
the resistance of the load by a factor of two would cause the
current to decrease by a factor of two to one-half its original
value.
Let’s practice: I = V / R
•
Volts
resistance
current
1. 1.5 V
3Ω
0.50 Amp
2. 3.0 V
3Ω
________
3. 4.5 V
3Ω
________
4. 4.5 V
6Ω
________
5. 4.5 V
9Ω
________
V and I have
direct
relationship
V and R
have inverse
relationship
example
• The diagram below depicts a couple of circuits
containing a voltage source (battery pack), a resistor
(light bulb) and an ammeter (for measuring current). In
which circuit does the light bulb have the greatest
resistance?
A
B
Circuit
• A path through which current flows from an area
of high voltage to an area of low voltage.
Circuit Elements
Voltage sources
Resistances
Measurement
Devices
Other Elements
Measurements
V
100V
R = 10Ω
V
10A
0V
Voltmeter
measures
RELATIVE
differences
from OUTSIDE
the circuit
10A
V
A 0V
A
V = 100V
V
100V
Ammeter
measures
flow INSIDE
the circuit
Graphs: I vs. V and I vs. R
I vs. V
I vs. R
Slope = ∆I / ∆V =
1/R
I
V
Current and potential difference
have a direct relationship. The
slope is equivalent to the
reciprocal of the resistance of
the resistor.
I
R
Current and
resistance have an
inverse relationship
Check Your Understanding
1. Which of the following will cause the current through an
electrical circuit to decrease? Choose all that apply.
a. decrease the voltage
b. decrease the resistance
c. increase the voltage
d. increase the resistance
2. A certain electrical circuit contains a battery with three
cells, wires and a light bulb. Which of the following would
cause the bulb to shine less brightly? Choose all that
apply.
a. increase the voltage of the battery (add another cell)
b. decrease the voltage of the battery (remove a cell)
c. decrease the resistance of the circuit
d. increase the resistance of the circuit
3.
A circuit is wired with a power supply, a resistor and an ammeter (for
measuring current). The ammeter reads a current of 24 mA
(milliAmps). Determine the new current if the voltage of the power
supply was ...
a. ... increased by a factor of 2 and the resistance was held constant.
b. ... increased by a factor of 3 and the resistance was held constant.
c. ... decreased by a factor of 2 and the resistance was held constant.
d. ... held constant and the resistance was increased by a factor of 2.
e. ... held constant and the resistance was increased by a factor of 4.
f. ... held constant and the resistance was decreased by a factor of 2.
g. ... increased by a factor of 2 and the resistance was increased by a
factor of 2.
h. ... increased by a factor of 3 and the resistance was decreased by a
factor of 2.
i. ... decreased by a factor of 2 and the resistance was increased by a
factor of 2.
4.
Use the Ohm's law equation to determine the missing
values in the following circuits.
6
How is current controlled in A & B?
4
How is current controlled in C & D?
example
• The graph shows the relationship between
current and potential difference for four resistors,
A, B, C, and D . Which resistor has the greatest
resistance?
example
• A series circuit has a total resistance of 1.00 ×
102 ohms and an applied potential difference of
2.00 × 102 volts. What is the amount of charge
passing any point in the circuit in 2.00 seconds?
example
• A long copper wire was connected to a voltage source.
The voltage was varied and the current through the wire
measured, while temperature was held constant. Using
the graph to find the resistance of the copper wire.
•
1.
2.
example
A student conducted an experiment to determine the
resistance of a light bulb. As she applied various potential
differences to the bulb, she recorded the voltages and
corresponding currents and constructed the graph below.
The student concluded that the resistance of the light bulb
was not constant.
What evidence from the graph supports the student’s
conclusion?
According to the graph, as the
potential difference increased,
what happens to the
resistance of the light bulb?
example
•
1.
2.
3.
4.
A circuit consists of a resistor and a battery.
Increasing the voltage of the battery while keeping the
temperature of the circuit constant would result in an
increase in
current, only
resistance, only
both current and resistance
neither current nor resistance
example
• Sketch a graph that best represents the
relationship between the potential difference
across a metallic conductor and the electric
current through the conductor
1. At constant temperature T1
2. At a higher constant temperature T2.
V
I
Lesson 4: Electrical Power
• Power: Putting Charges to Work
• Common Misconceptions Regarding
Electric Circuits
Power: Putting Charges to Work
• Electric circuits are designed to serve a useful function. The
mere movement of charge from terminal to terminal is of
little use if the electrical energy possessed by the charge is
not transformed into another useful form.
• To equip a circuit with a battery and a wire leading from
positive to negative terminal without an electrical device
(light bulb, beeper, motor, etc.) would lead to a high rate of
charge flow. Such a circuit is referred to as a short circuit. It
would heat the wires to a high temperature and drain the
battery of its energy rather quickly.
• When a circuit is equipped with a light bulb, beeper, or
motor, the electrical energy supplied to the charge by the
battery is transformed into other forms in the electrical
device. These electrical devices are generally referred to as
a load.
Electrical Power
• An electrical circuit is simply an energy transformation
tool. Energy is provided to the circuit by an electrical
energy source, and energy is delivered by the circuit to
the load. The rate at which this energy transformation
occurs called Power.
• Power is the rate at which electrical energy is supplied
to a circuit or consumed by a load. electrical power, like
mechanical power, is the rate at which work is done. Like
current, power is a rate quantity. It's mathematical
formula is expressed on a per time basis.
• The unit of power is watt.
• One watt of power is equivalent to the delivery of
1 joule of energy every second. In other words: 1
watt = 1 joule / second
• A 60 watts light bulb means 60 joules of energy
delivered to the light bulb every second. A 120watt light bulbs draws 120 joules of energy every
second.
The kilowatt-hour
• Electrical utility companies who provide energy for
homes provide a monthly bill charging those homes for
the electrical energy which they used. A typical bill will
contain a charge for the number of kilowatt-hours of
electricity which were consumed.
• 1 Kilowatt = 1,000 watt, which represent power.
• 1 hour = 3,600 seconds, which represent time.
• A kilowatt • hour is a unit of Power • time.
• Since P = E / t, therefore P• t = E.
• So the kilowatt • hour is a unit of energy.
• 1 Kwh = (1,000 w)(3,600 s) = 3,600,000 J
misconception
• True or False?
• The utility company provides electricity in the
form of electrons.
Calculating Power
When we combine the equations above, we can derive:
• The electrical power is simply the product of the electric
potential difference and the current.
The two quantities that power depends upon are both related to
the resistance of the load by Ohm's law.
∆V = (I • R)
I = ∆V / R
By combing Ohm’s law and the equation for power (P = ∆V∙I), two
new equations can be derived that relate the power to the current
and the resistance and to the electric potential difference and the
resistance.
P = I2 • R
P = ∆V2 / R
P = I2•R
P = V2/R
P = V·I
relate current and resistance to power, notice double
importance of current.
relate potential difference and resistance to power,
notice double importance of potential difference.
relate potential difference and current to power.
Notice that both have equal importance.
While these three equations provide one with convenient
formulas for calculating unknown quantities in physics
problems, one must be careful to not misuse them by ignoring
conceptual principles regarding circuits.
example
• If a 60-watt bulb in a household lamp was replaced
with a 120-watt bulb, then how many times greater
would the current be in that lamp circuit?
Graphs of power vs. R, I, V
• P = VI = I2R = V2/R
• When V is constant: P = VI; P = V2/R
P
P
Inverse, high R, low P
V is slope
R
I
• When R is constant: P = I2R; P = V2/R
P
P
Direct squared
I
Direct squared
V
example
• Which is a unit of electrical power?
1.volt/ampere
2.ampere/ohm
3.ampere2/ohm
4.volt2/ohm
example
• As the resistance of a constant-voltage
circuit is increased, the power developed
in the circuit
1.decreases
2.increases
3.remains the same
example
• The potential difference applied to a circuit element remains
constant as the resistance of the element is varied. Graph
power (P) vs. resistance ((R) for this circuit.
P
R
example
• Graph the relationship between the
electrical power and the current in a
resistor that obeys Ohm’s Law.
P
I
example
• An electric motor uses 15 amperes of
current in a 440-volt circuit to raise an
elevator weighing 11,000 newtons. What
is the average speed attained by the
elevator?
Statement True or False?
1. When an electrochemical cell no longer works, it is out of
charge and must be recharged before it can be used again.
2. An electrochemical cell can be a source of charge in a
circuit. The charge which flows through the circuit originates
in the cell.
3. Charge becomes used up as it flows through a circuit. The
amount of charge which exits a light bulb is less than the
amount which enters the light bulb.
4. Charge flows through circuits at very high speeds. This
explains why the light bulb turns on immediately after the
wall switch is flipped.
5. The local electrical utility company supplies millions and
millions of electrons to our homes everyday.
Rechargeable Batteries
• Rechargeable batteries has nothing to do with charges.
• A battery (or single cell) operates by packing a collection of reactive
chemicals inside. These chemicals undergo a reaction that
produces energy. This energy-producing reaction is capable of
pumping the charge through the battery from low energy terminal to
high energy terminal and establishing the electric potential
difference across the external circuit. When a battery no longer
works, it is because the chemicals have been consumed to the
point that the ability of the battery to move the charge between
terminals has been severely diminished.
• Rechargeable batteries rely upon a reversible reaction, turning
the chemical products back into chemical reactants within the cell.
• By placing the cell into a so-called recharger, the energy of a
household electrical circuit can be used to drive the reaction in the
reverse direction and transform the chemical products back into
chemical reactants. This reverse process requires energy; it is the
recharger which supplies the energy. With reactants replenished,
the cell can now be used again to power the electric circuit.
Quantities, Symbols, Equations and
Units!
• The tendency to give attention to units is an
essential trait of any good physics student.
• Many of the difficulties associated with
solving problems may be traced back to the
failure to give attention to units. As more and
more electrical quantities and their respective
metric units are introduced, it will become
increasingly important to organize the
information in your head.
Symbol
Equations
Standard
Metric
Unit
V
V= W / Q
V=I•R
Volt (V)
J/C
I
I=Q/t
I=V/R
Amperes
(A)
C/s
V/Ω
P
P=W/t
P = V∙I
P = V2/R
P = I2R
Watt (W)
J/s
V∙A
V/ Ω2
A2∙Ω
Resistance
R
R = ρ•L / A
R=V/I
Ohm (Ω )
V/A
Energy
W
W=V•Q
W=P•t
Joule (J)
V•C
W•s
Quantity
Potential
Difference
(a.k.a. voltage)
Current
Power
Other
Units
Check Your Understanding
• The purpose of every circuit is to supply the energy to
operate various electrical devices. These devices are
constructed to convert the energy of flowing charge into
other forms of energy (e.g., light, thermal, sound,
mechanical, etc.). Use complete sentences to describe
the energy conversions that occur in the following
devices.
a. Windshield wipers on a car
b. Defrosting circuit on a car
c. Hair dryer
example
• To increase the brightness of a desk lamp,
a student replaces a 60-watt light bulb with
a 100-watt bulb. Compared to the 60-watt
bulb, the 100-watt bulb has
1.less resistance and draws more current
2.less resistance and draws less current
3.more resistance and draws more current
4.more resistance and draws less current
Check Your Understanding
1. Which would be thicker (wider) - the filament of a 60-Watt light
bulb or the filament of a 100-W light bulb? Explain.
2. Calculate the resistance and the current of a 7.5-Watt night light
bulb plugged into a US household outlet (120 V).
Electrical energy
• E = P∙t = V∙I∙t = I2∙R∙t = (V2/R)∙t
• The SI unit for energy is ___________.
joule
• 1 joule = (1 Newton)(1 meter)
= (1 kg∙m/s2)(1 meter)
= 1 kg∙m2/s2
example
• Your 60-watt light bulb is plugged into a 110-volt
household outlet and left on for 10 hours. The utility
company charges you $0.20 per kiloWatt•hr. What is the
cost of such a mistake.
example
• A current of 0.40 ampere is measured in a
150 ohm resistor, how much energy is
expended by the resistor in 20. seconds?
example
• An operating 75-watt lamp is connected to
a 120-volt outlet. How much electrical
energy is used by the lamp in 60. minutes
(3600 seconds)?
example
• An electric dryer consumes 6.0 × 106
joules of energy when operating at 220
volts for 30. minutes (1800 seconds).
During operation, how much current does
the dryer draws approximately?
example
• 50.-ohm resistor, an unknown resistor R, a 120-volt source, and
an ammeter are connected in a complete circuit. The ammeter
reads 0.50 ampere. Calculate the power dissipated by the 50.ohm resistor.
example
• The heating element on an electric stove
dissipates 4.0 × 102 watts of power when
connected to a 120-volt source. What is the
electrical resistance of this heating element?
3/6 DO NOW
•
1.
2.
3.
4.
A copper wire is connected across a
constant voltage source. The current
flowing in the wire can be increased by
increasing the wire's
cross-sectional area
length
resistance
temperature
objectives
• Circuit connections
• No post today
Lesson 4: Circuit Connections
1.
2.
3.
4.
Circuit Symbols and Circuit Diagrams
Two Types of Connections
Series Circuits
Parallel Circuits
Circuit Symbols
Voltage sources
Resistances
Measurement
Devices
Other Elements
Example 1:
Description with Words:
• Three D-cells are placed in a battery pack to
power a circuit containing three light bulbs
Only use circuit symbols in your reference table to
draw the circuits
Example 2:
• Description with Words: Three D-cells are
placed in a battery pack to power a circuit
containing three light bulbs.
Two types of connections
• These two examples illustrate the two common
types of connections made in electric circuits.
When two or more resistors are present in a
circuit, they can be connected in series or in
parallel.
Lab 27 – two types of circuits
• Go to: http://phet.colorado.edu/en/simulation/circuitconstruction-kit-dc
Purpose: compare series and parallel circuits
Material: computer
1. Draw schematic diagrams for series and parallel circuits
consisting of 3 light bulbs.
2. As the light bulbs are added, what happens to the
current going to the battery
3. As the light bulbs are added, what happens to the total
resistance of the circuit?
4. If one light bulb is taken out, what happens to the other
light bulbs?
For series circuits
1. As more resistors are added the overall
current within the circuit decreases.
2. This decrease in current is consistent with the
conclusion that the overall resistance
increases.
3. If one of three bulbs in a series circuit is
unscrewed from its socket, then the other
bulbs immediately go out.
For parallel circuits
1. As the number of resistors increases, the
overall current also increases.
2. This increase in current is consistent with a
decrease in overall resistance. Adding more
resistors in a separate branch has the
unexpected result of decreasing the overall
resistance!
3. If an individual bulb in a parallel branch is
unscrewed from its socket, then there is still
current in the overall circuit and current in
the other branches.
The effect of adding resistors
• Adding more resistors in series means
that there is more overall resistance;
• Adding more resistors in parallel means
that there is less overall resistance.
Check Your Understanding
1. Observe the electrical wiring below. Indicate whether
the connections are series or parallel connections.
Explain each choice.
2. Two electric circuits are diagrammed below. For
each circuit, indicate which two devices are
connected in series and which two devices are
connected in parallel.
In series? ______________
In parallel? ______________
In series ________________
In parallel? ______________
Series circuit
• A series circuit is a circuit in which all parts are
single
connected end to end to provide a ___________
path for
the current.
• The figure shows three resistors connected in series with
a battery. The resistors are differentiated by the use of
subscripts R1, R2, and R3.
Adding more resistors to
a series circuit results in
more overall resistance.
This increased
resistance serves to
reduce the rate at which
charge flows (also
known as the current).
Current
• Since there is only one current path in a
series circuit, the current is the same
through each resistor.
Ibattery = I1 = I2 = I3 = ..
•
______________________
Charge flows together
through the external circuit
at a rate which is
everywhere the same. The
current is no greater at one
location as it is at another
location.
Equivalent Resistance
• The equivalent resistance of a circuit is the amount of
resistance which a single resistor would need in order to
equal the overall affect of the collection of resistors
which are present in the circuit.
•The equivalent resistance in a series circuit is the sum of the
circuit’s resistances:
Req = R1 + R2 + R3 + ...
____________________________________
Potential Difference and Voltage Drops
• The sum of the potential differences across the
individual resistors equals the applied potential
difference at the terminals.
∆V
=
∆V
+
∆V
+
∆V
+
...
battery
1
2
3
• _______________________________
Mathematical Analysis of Series
Circuits
Ibattery= I1 = I2 = I3 = ...
Req = R1 + R2 + R3 + ...
Vbattery = V1 + V2 + V3 + ...
• All COMPONENTS and the WHOLE CIRCUIT obey
Ohm’s Law
V1
V =I•R
V =I•R
V =I•R
1
1
2
2
3
3
V2
V3
example
40
1.5
1.5
25.5
1.5
18
1.5
16.5
example
• The diagram represents a series circuit
containing three resistors. What is the current
through resistor R2?
I = V / R = 3.0 V / 9.0 Ω
I = 0.33 A
example
• In the circuit shown in the diagram, what is the
correct reading for meter V2?
V = V1 + V2 + V3
110 V = 20 V + V2 + 20 V
V2 = 70 V
example
• A series circuit has a total resistance of
1.00 x 102 ohms and an applied potential
difference of 2.00 x 102 volts. What is the
amount of charge passing any point in the
circuit in 2.00 seconds?
I = V / R = 2.00 x 102 V / 1.00 x 102 Ω
I = 2.00 A
I=Q/t
2.00 A = Q / 2.00 s
Q = 4.00 C
3/7 do now
1.
2.
3.
4.
Draw a schematic diagrams for series circuits consisting
of 3 lamps.
As lamps are added, what happens to the total current
going to the battery.
As lamps are added, what happens to the total
resistance of the circuit?
If one lamp is taken out, what happens to the other light
lamps?
Homework
questions?
objectives
• Series circuits
• Parallel circuits
• Lesson 4, 5 quiz on castle learning – due
Monday
One by One
Series Circuits
Series Circuit
A circuit composed of two or more elements
connected end-to-end.
Rules
• The equivalent resistance for a series circuit is the
SUM of all RESISTANCES in the circuit
• Req = R1 + R2 + R3 + …+ RN
• The total voltage in the circuit is equal to the SUM of
the VOLTAGE DROPS across the resistors.
• VT = V1 +V2 + V3 + …+ VN
• The current in the circuit is constant at ALL points
in the circuit.
• IT = I1 = I2 = I3 = …= IN
• All COMPONENTS and the WHOLE CIRCUIT obey
Ohm’s Law
Req = R1 + R2 + R3 = 400Ω
100 Ω
75 Ω
225 Ω
R1
R2
R3
10 V
I=V/R
I = 10 V / 400 Ω
I = 0.025 A
VIRP Chart
V
I
R
P
2.5V
0.025A
100Ω
0.063W
R2
1.875V 0.025A
75Ω
0.047W
R3
5.625V 0.025A
225Ω
0.14W
400Ω
0.25W
R1
Req
10V
0.025A
50 Ω
120 Ω
150 Ω
R1
R2
R3
1.5A
?V
VIRP Chart
V
I
R
P
R1
75 V
1.5A
50Ω
112.5W
R2
180 V
1.5A
120Ω
270.0W
R3
225 V
1.5A
150Ω
337.5W
Req
480 V
1.5A
320Ω
720W
homework
• Practice packet page 28-30
• Due tomorrow – pp. 23-30
• Check List Packet – (please label you
packet) – pp. 1-3
3/11 do now – on a new sheet
R1, R2, and R3 are connected in a series circuit with
the following given quantities. Fill in the missing
data.
V
I
R
R1
50Ω
R2
100Ω
R3
150Ω
Req
1.0A
P
objectives
• Homework due – pp. 23-30
• Lab – series circuits
• Parallel circuits
• Homework – pp. 31-34
• T-shirt money is due ASAP
Parallel circuits
• A parallel circuit is a circuit in which If two
or more circuit components are connected
rungs of a ladder.
like the _______________________.
• Unlike in series circuit, there is just one
path for current flow, in a parallel circuit,
two or more
there are ____________________
paths
for current flow.
1. More current flows through the smaller resistor. (More
charges take the easiest path.)
2. The potential difference of different resistors are the
same, they all have the same drop.
3. By the time each charge makes it back to the battery, it has
lost all the electrical energy given to it by the battery.
Current
• In a parallel circuit, charge divides up into separate
branches such that there can be more current in one
branch than there is in another. Nonetheless, when
taken as a whole, the total amount of current in all the
branches when added together is the same as the
amount of current at locations outside the branches.
• In equation form, this principle can be written as
• Itotal = I1 + I2 + I3 + ...
• where Itotal is the total amount of current outside the
branches (and in the battery) and I1, I2, and I3
represent the current in the individual branches of the
circuit.
• At any junction in a circuit, the sum of the currents
entering the junction must equal the sum of current
leaving it.
This is the symbol for an ammeter - a device
used to measure the current at a specific point.
An ammeter is capable of measuring the current
while offering negligible resistance to the flow of
charge.
Kirchhoff’s law - conservation of charge
(Junction Rule)
• The sum entering any current junction, is equal to the
sum leaving. A represents a junction in an electric
circuit. Nine amperes are entering A: therefore,
according to Kirchhoff’s First Law, nine amperes must
come out of junction A.
6 amp
9 amp
A
3 amp
example
•
1.
2.
3.
4.
The diagram shows the current in three of the branches
of a direct current electric circuit. The current in the
fourth branch, between junction P and point W, must be
1 A toward point W
1 A toward point P
7 A toward point W
7 A toward point P
example
•
The diagram shows a current in a
segment of a direct current circuit. What
is the reading of ammeter A?
example
• The diagram below represents currents in
a segment of an electric circuit.
• What is the reading of ammeter A?
Equivalent Resistance
• For parallel circuit, adding more resistors results in the
rather unexpected result of having less overall
resistance.
• The equivalent resistance (total resistance) of a circuit
is the amount of resistance which a single resistor
would need in order to equal the overall effect of the
collection of resistors which are present in the circuit.
For parallel circuits, the mathematical formula for
computing the equivalent resistance (Req) is
1
1
1
1
 

Req R1 R2 R3
where R1, R2, and R3 are the resistance values of the
individual resistors which are connected in parallel.
example
1/Req = 1/(5.0 Ω) + 1/(7.0 Ω) + 1/(12 Ω)
Req = 2.3 Ω
Note: the equivalent resistance is less than any single
resistance in the circuit.
example
• Which circuit segment below has the same total
resistance as the circuit segment shown in the
diagram?
1
2
3
4
example
• Resistors R1 and R2 have the same resistance.
When they are connected together as shown,
they have an equivalent resistance of 4
ohms. What is the resistance of R1?
Since R1 = R2
1/4 Ω = 1/R1 + 1/R1 = 2/R1
R1 = 8 Ω
Note: the equivalent resistance is smaller
than any single resistance in the parallel
circuit.
example
•
1.
2.
3.
4.
Resistors R1 and R2 have an equivalent
resistance of 6 ohms when connected as
shown. What is the resistance of R1?
3 ohms
4 ohms
5 ohms
8 ohms
Since the equivalent resistance is smaller
than any single resistance in the parallel
circuit, the answer is 8 ohms
Voltage Drops for Parallel Branches
• The total voltage drop in the external circuit is equal to
the gain in voltage as a charge passes through the
internal circuit. In a parallel circuit, a charge does not
pass through every resistor; rather, it passes through a
single resistor. Thus, the entire voltage drop across that
resistor must match the battery voltage. It matters not
whether the charge passes through resistor 1, resistor 2,
or resistor 3, the voltage drop across the resistor which it
chooses to pass through must equal the voltage of the
battery. Put in equation form, this principle would be
expressed as V
battery = V1 = V2 = V3 = ..
• The current through a given branch can be predicted
using the Ohm's law equation and the voltage drop
across the resistor and the resistance of the resistor.
Since the voltage drop is the same across each resistor,
the factor which determines which resistor has the
greatest current is the resistance. The resistor with the
greatest resistance experiences the lowest current
and the resistor with the least resistance experiences the
greatest current. In this sense, it could be said that
charge (like people) chooses the path of least
resistance. In equation form, this could be stated as
I1 = V / R1
I2 = V / R2
I3 = V / R3
In a parallel circuit:
1. The potential drops of each branch equals the potential
rise of the source.
2. The total current is equal to the sum of the currents in
the branches.
3. The inverse of the total resistance of the circuit (also
called equivalent resistance) is equal to the sum of
the inverses of the individual resistances.
4. All COMPONENTS and the WHOLE CIRCUIT obey
Ohm’s Law
example
• Find the voltage drop R1, R2, and R3
• Find the current in R1, R2, and R3
example
4.3
14.0
3.5
60.
5.0
60.
5.5
60.
example
• A 9.0 V battery is connected in parallel to
four light bulbs with resistances 4.0Ω,
5.0Ω, 2.0Ω, and 7.0Ω. Find the equivalent
resistance for the circuit and the total
current in the circuit.
Req = 0.92 Ω
I = 9.8 A
example
•
What are the readings on the volt meters in A & B?
A
B
Parallel circuits,
VT = V1 = V2 = 6 V
Series circuits,
VT = V1 + V2 = 6 V;
I1 = I2 ;
V1 /R1 = V2 / R2;
V1 /20 = V2 /40
V1 = 2 Volts
example
• In the diagram, what is the potential
difference across the 3.0-ohm resistor?
3/12 do now
•
The diagram represents a series circuit
containing three resistors. What is the current
through resistor R2?
Show work
Homework
questions?
objectives
• Parallel circuits
• Meters in a circuits
• Homework – practice packet pp. 35-40
example
•
Circuit A and circuit B are shown in the
diagram. Compared to the total resistance of
circuit A, the total resistance of circuit B is
1. less
2. greater
3. the same
example
•
1.
2.
3.
4.
A physics student is given three 12-ohm
resistors with instructions to create a circuit that
would have the lowest possible
resistance. The correct circuit would be
a series circuit with a total resistance of 36
ohms
a series circuit with a total resistance of 4 ohms
a parallel circuit with a total resistance of 36
ohms
a parallel circuit with a total resistance of 4
ohms
Meters in a circuit
• Ammeters, as well as voltmeters and ohmmeters, are designed with the use of a
galvanometer
_______________________,
which is sensitive
electric current detector.
• When a current is passed through a coil in a
magnetic field, the coil experiences a torque
proportional to the current.
Meters in a circuit
current
• An ammeter is used to measure ____________
series with
• An ammeter is always connected in __________
the circuit element being measured
• A voltmeter is used to measure
potential
difference.
________________________________
parallel.
• A voltmeter is always connected in __________.
ammeter
• An ammeter is placed in series with a
circuit element to measure the electric
current flow through it. The meter must be
very little
designed offer ________________
resistance to the current so that it does
not change the circuit it is measuring.
example
• In the diagram of a parallel circuit,
ammeter A measures the current supplied
by the 110-volt source. What is the
current measured by ammeter A?
11 A
example
• Two resistors are connected to a source of
voltage as shown in the diagram. At which
position should an ammeter be placed to
measure the current passing only through
resistor R1?
1. position 1
2. position 2
3. position 3
4. position 4
example
• Three ammeters are placed in a circuit as
shown in the diagram. If A1 reads 5.0
amperes and A2 reads 2.0 amperes, what
does A3 read?
3A
voltmeter
• A voltmeter is placed in parallel with a circuit element to
measure the voltage drop across it and must be
designed to draw very little current from the circuit so
that it does not appreciably change the circuit it is
measuring. A voltmeter has a big resistance, so it does
not affect the overall circuit.
example
• In the circuit shown in the diagram, which
is the correct reading for meter V2?
example
• Which circuit could be used to determine the
total current and potential difference of a parallel
circuit?
A
C
B
D
example
• In the circuit shown in the diagram, what is
the potential difference of the source?
meters
Read current, connected in series, very
low resistance
ammeter
Read potential difference, connected in
parallel, very high resistance
voltmeter
Wiring for Voltage
Parallel Circuits
Parallel Circuits
A circuit in which all of the resistors are connected “in parallel”
to the same voltage source.
Note: in this animation that the charges have the same potential
before and after they pass through the resistors!
Parallel Circuits
The charges fall through the 30Ω resistor at a slower rate.
Less CURRENT flows through that branch of the circuit!
The CURRENT flowing into and out of the BATTERY
is the same!
Rules
• The inverse of the equivalent resistance is the sum of
the INVERSES OF EACH RESISTANCE
1
1
1
1
1



 ... 
Req
R1
R2
R3
RN
• The total current in the circuit is equal to the SUM
of the CURRENT passing through each resistor.
I
 I1  I 2  I 3  ...  I N
• The voltage is the same for ALL resistors in the
circuit.
V  V1  V2  V3  ...  VN
• All COMPONENTS and the WHOLE CIRCUIT obey
Ohm’s Law
Junction Rule
The total current flowing INTO a junction of two or more
wires is the SAME as the total current flowing OUT
of the junction.
10A
?
5A
5A
Junction Rule
6A
?
6A
?
4A
2A
10A
V
I
R1
60 V
2A
30 Ω 120W
R2
60 V
2A
30 Ω 120 W
R3
60 V
2A
30 Ω 120 W
Req
60 V
6A
10 Ω 360W
R3 = 30 Ω
R2 = 30 Ω
R1 = 30 Ω
60 V
R
P
R3 = 50 Ω
R2 = 60 Ω
R1 = 70 Ω
?V
V
0.05 A
R1
R2
R3
Req
I
R
P
2.5 V
0.036A 70 Ω
0.09W
2.5 V
0.042A 60 Ω
0.11 W
2.5 V
0.05A
2.5 V
0.128A 19.62 Ω 0.32W
50 Ω 0.13 W
3/13 do now
• A lamp and an ammeter are connected to a source as
shown in the diagram. What is the electrical energy
expended in the lamp in 3.0 seconds? [show work]
objectives
• Homework questions - Packet pp. 31-40 is
due
• Finish series circuits lab
• Homework: Electric current check list
• Castle learning quiz – due Friday
• Electromagnetism Unit Test is on Tuesday
example
• Which circuit below would have the lowest
voltmeter reading?
A
B
C
D
example
•
1.
2.
3.
4.
In which pair of circuits shown in the diagram could the
readings of voltmeters V1 and V2 and ammeter A be correct?
A and B
B and C
C and D
A and D
example
• In the circuit diagram below, what are the
correct readings of voltmeters V1 and V2?
6V
example
•
1.
2.
3.
4.
Which statement about ammeters and voltmeters is
correct?
The internal resistance of both meters should be low.
Both meters should have a negligible effect on the
circuit being measured.
The potential drop across both meters should be
made as large as possible.
The scale range on both meters must be the same.
example
•
In the diagram below, lamps L1 and L2 are
connected to a constant voltage power supply. If
lamp L1 burns out,
1. What will happen to the equivalent resistance of
the circuit?
2. What will happen to the total current of the circuit?
3. What will happen to the brightness of L2 ?
example
• Identical resistors (R) are connected across the same
12-volt battery. Which circuit uses the greatest power?
A
C
B
D
• Three identical light bulbs are connected to a D-cell as
shown below. P, Q, X, Y and Z represent locations along
the circuit. Which one of the following statements is true?
a. The current at Y is greater than the current at Q.
b. The current at Y is greater than the current at P.
c. The current at Y is greater than the current at Z.
d. The current at P is greater than the current at Q.
e. The current at Q is greater than the current at P.
f. The current is the same at all locations.
• Three identical light bulbs are connected to a Dcell as shown below. P, Q, X, Y and Z represent
locations along the circuit. At which location(s), if
any, will the current be ...
a. ... the same as at X?
b. ... the same as at Q?
c. ... the same as at Y?
d. ... less than at Q?
e. ... less than at P?
f. ... twice that at Z?
g. ... three times that at Y?
• Which adjustments could be made to the circuit
below that would decrease the current in the
cell? List all that apply.
a. Increase the resistance of bulb X.
b. Decrease the resistance of bulb X.
c. Increase the resistance of bulb Z.
d. Decrease the resistance of bulb Z.
e. Increase the voltage of the cell (somehow).
f. Decrease the voltage of the cell (somehow).
g. Remove bulb Y.
• Draw a diagram that shows voltmeter V and ammeter A
correctly positioned to measure the total current of the
circuit and the potential difference through each resistor.
V
A
Lab 28 – investigating series circuit
Objective: to study the relationships among resistance, voltage, and
current when resistors are connected in a series circuit.
Material: D.C. power supply, resistance board, D.C ammeter,
multipurpose meter, connecting wires.
Procedure: Briefly describe how the lab is going to be done. Draw
diagrams to show how to measure each variable (one diagram
for each rariable). Someone who was not present during the lab
should be able to understand how the experiment was perforem
and be able to reporduce the results by reading your procedure
Data section: should contain colomns of measured and calculated
data. The columns should be labeled; units should be identified.
Conclusion: The Conclusion should (as always) answer the questions
posed in the Purpose:
1. How does the total resistance and resistance in RD, RE, RF
compare?
2. How does the total current and current in RD, RE, RF compare?
3. How does the total voltage and voltage drop in RD, RE, RF
compare?
data table
Current (A)
Resistor D
Resistor E
Resistor F
equivalent
Voltage (V)
Resistance
(ohms)
R
R
Resistance in
E
Resistance in
D
D
E
F
D
E
F
Measuring resistance
R
Resistance in
F
R
Total
resistance
D
E
F
D
E
F
V
Measuring voltage
Voltage
in D
V
Voltage
in E
D
E
F
D
E
F
Source
Source
V
Voltage
in F
V
D
E
F
Source
Total
Voltage
D
E
F
Source
Total
current
Current
in D
D
E
F
D
E
F
Source
Source
A
Measuring
current Current
Current
in E
A
A
in F
D
E
F
Source
D
E
F
Source
A
3/13 do now
• A lamp and an ammeter are connected to a source as
shown in the diagram. What is the electrical energy
expended in the lamp in 3.0 seconds? [show work]
objectives
• Homework questions - Packet pp. 31-40 is due
• Finish series circuits lab
• Homework: Electric current check list
• Castle learning quiz – due Friday
• Electromagnetism Unit Test is on Tuesday and
Wednesday.
• T-shirt money is due! (Anyone want to buy T-shirt?)
Lab 30 – investigating parallel circuit
Objective: to study the relationships among resistance, voltage, and
current when resistors are connected in a parallel circuit.
Material: Computer, PHeT wet site
Procedure: Go to PHeT website, construct a parallel circuits with 3
different resistors, RD, RE, RF . Copy the diagram in your lab note
book.,. Measure total current and current in each resistor with
ammeters, indicate ammeter in your diagram. Measure total voltage
and voltage across each resistor with a voltmeter and indicate
voltmeter in your diagram.
Data section: should contain colomns of measured and calculated data.
The columns should be labeled; units should be identified.
Conclusion: The Conclusion should (as always) answer the questions
posed in the Purpose:
1. How does the total resistance and resistance in RD, RE, RF compare?
2. How does the total current and current in RD, RE, RF compare?
3. How does the total voltage and voltage drop in RD, RE, RF compare?
Lab 20 data table
Current (A) Voltage (V) Resistance
(ohms)
Resistor D
Resistor E
Resistor F
equivalent
3/11 do now – on a new sheet
R1, R2, and R3 are connected in a series circuit with
the following given quantities. Fill in the missing
data.
V
I
R
R1
50Ω
R2
100Ω
R3
150Ω
Req
1.0A
P
objectives
• Homework due – pp. 23-30
• Meters in circuits
• Homework – pp. 31-34
• T-shirt money is due ASAP
• Castle learning quiz is due today