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Chapter 18 & 19
Current , DC Circuits
Current is defined as the flow of positive
charge.
I = Q/t
I: current in Amperes or Amps (A)
Q: charge in Coulombs (C)
t: time in seconds (s)
Charge carriers
In a normal electrical circuit, it is the
electrons that carry the charge.
So if the electrons move this way, which
way does the current move?
Sample problem
How many electrons per hour flow past a
point in a circuit if it bears 11.4 mA of direct
current?
If the electrons are moving north, in which
direction is the current?
Circuit Components
Cell
• Cells convert chemical energy into electrical energy.
• The potential difference (voltage) provided by a cell is
called its electromotive force (or emf).
• The emf of a cell is constant, until near the end of the
cell’s useful lifetime.
• The emf is not really a force. It’s one of the biggest
misnomers in physics!
Battery
• A battery is composed of more than one cell in series.
• The emf of a battery is the sum of the emf’s of the
cells.
Sample problem
If a typical AA cell has an emf of 1.5 V,
how much emf do 4 AA cells provide?
Draw the battery composed of these 4
cells.
Circuit Components
Sample Problem:
Draw a single loop circuit that contains a
cell, a light bulb, and a switch.
Label the components.
Now put a voltmeter in the circuit so it reads
the potential difference across the light bulb.
Series arrangement of components
Series components are put together so
that all the current must go through each
one
Parallel arrangement of components
Parallel components are put together so that the
current divides, and each component gets only a
fraction of it.
Sample Problem:
Draw a circuit having a cell and four bulbs.
Exactly two of the bulbs must be in parallel.
Minilab #1
Draw a circuit containing one cell, one bulb,
and a switch.
Create this in the PhET simulation.
Measure the voltage across the cell and
across the bulb. What do you observe?
Minilab #2
Draw a circuit containing two cells in series, one bulb,
and a switch.
Create this in the PhET simulation.
What do you observe happens to the bulb (compared
to minilab #1)?
Measure the voltage across the battery and across
the bulb.
What do you observe?
Minilab #3
Draw a circuit containing two cells in series, two
bulbs in series, and a switch.
Create this in the PhET simulation.
What do you observe happens to the bulbs when
you disconnect one of the bulbs? ( or open the
switch)?
Measure the voltage across the battery and
across each bulb.
What do you observe?
Minilab #4
Draw a circuit containing two cells in series, two
bulbs in parallel, and a switch right next to one of
the bulbs.
Create this in the PhET simulation.
What do you observe happens to the bulbs when
you disconnect one bulb (or open the switch)?
Measure the voltage across the battery and
across each bulb.
What do you observe?
General Rules
How does the voltage from a cell or battery get
dispersed in a circuit…
when there is one component?
when there are two components in series?
when there are two components in parallel?
Ohm’s Law and Resistivity
Conductors
•
•
•
•
•
Conduct electricity easily.
Have high “conductivity”.
Have low “resistivity”.
Metals are examples.
Wires are made of conductors
Insulators
•
•
•
•
Don’t conduct electricity easily.
Have low “conductivity”.
Have high “resistivity”.
Rubber is an example.
Resistors
• Resistors are devices put in circuits to reduce
the current flow.
• Resistors are built to provide a measured
amount of “resistance” to electrical flow, and
thus reduce the current..
Sample problem
Draw a single loop circuit containing two
resistors and a cell. Draw voltmeters
across each component.
Resistance, R
Resistance depends on resistivity and on
geometry of the resistor.
R = ρL/A
ρ: resistivity (Ω m)
L: length of resistor (m)
A: cross sectional area of resistor (m2)
Unit of resistance: Ohms (Ω)
Analogy to flowing water
Resistivities (ρ) of common materials
Silver
Copper
Aluminum
Iron
Nichrome
Carbon
Drinking Water
Hard Rubber
Air
1.59 x 10-8 Ωm
1.72 x 10-8 Ωm
2.82 x 10-8 Ωm
10.0 x 10-8 Ωm
100 x 10-8 Ωm
3500 x 10-8 Ωm
2 x 102 Ωm
1 x 1013 Ωm
1 x 1016 Ωm
Sample problem
What is the resistivity of a substance which
has a resistance of 1000Ω if the length of the
material is 4.0cm and its cross sectional area
is 0.20 cm2?
Ohm’s Law
Resistance in a component in a circuit causes
potential to drop according to the equation:
ΔV = IR
ΔV: potential drop/difference (Volts)
I: current (Amperes)
R: resistance (Ohms)
The drop in potential occurs as electrical energy is
transformed to other forms (heat, light) and work is
done.
Sample problem
Determine the current through a 333Ω resistor
if the voltage drop across the resistor is
observed to be 1.5 V.
Sample problem
• Draw a circuit with a AA cell attached to a
light bulb of resistance 4Ω.
• Determine the current through the bulb.
(Calculate)
Power
P = W/t
P = ΔE/Δt
P = I ΔV
P: power (W)
I: current (A, C/s)
ΔV: potential difference (V, J/C)
P = I 2R
P = (ΔV)2/R
Units:
Watts OR Joules/second
Sample problem
How much current flows through a 100-W light
bulb connected to a 120 V DC power supply?
What is the resistance of the bulb?
Sample problem
If electrical power is 5.54 cents per kilowatt hour,
how much does it cost to run a 100 W light bulb
for 24 hours?
Resistors in circuits
• Resistors can be placed in circuits in a variety of
arrangements in order to control the current.
• Arranging resistors in series increases the
resistance and causes the current to be
reduced.
• Arranging resistors in parallel reduces the
resistance and causes the current to increase.
• The overall resistance of a specific grouping of
resistors is referred to as the equivalent
resistance.
Resistors in series
R1
• Individual currents
add to total current
• Voltage drop is the
same across each
resistor
Resistors in parallel
Minilab #5
What is the equivalent resistance of a 100 Ω,
a 330 Ω and a 560 Ω resistor when these are
in a parallel arrangement?
(Draw, build a circuit in PhET, measure, and
calculate. Compare measured and calculated
values.)
Minilab #6
• Set up your digital multi-meter to measure resistance.
Measure the resistance of each of three light bulbs.
Record the results.
• Wire the three bulbs together in series, and draw this
arrangement. Measure the resistance of all three bulbs
together in the series circuit. How does this compare to
the resistance of the individual bulbs? Confirm
measurement with a calculation.
• Wire the three bulbs together in parallel, and draw this
arrangement. Measure the resistance of the parallel
arrangement. How does this compare to the resistance
of the individual bulbs? Confirm measurement with a
calculation.
Minilab #8
• Draw and build an arrangement of resistance that uses
both parallel and series arrangements for 5 or 6 resistors in
your kit. Calculate and then measure the equivalent
resistance. Compare the values.
Sample Problem
Draw a circuit containing, in order
(1) a 1.5 V cell, (2) a 100Ω resistor,
(3) a 330 Ω resistor in parallel with a 100 Ω resistor
(4) a 560 Ω resistor, and (5) a switch.
a) Calculate the equivalent resistance.
b) Calculate the current through the cell.
c) Calculate the current through the 330Ω resistor.
Resistors in Series and in Parallel
An analogy using
water may be helpful
in visualizing
parallel circuits:
Kirchhoff’s Rules
Some circuits cannot be broken down into
series and parallel connections.
Kirchhoff’s 1st Rule
For these circuits we use Kirchhoff’s rules.
Kirchhoff’s 1st Rule, Junction rule: The sum of currents
entering a junction equals the sum of the currents leaving
it (conservation of charge).
Sample problem
Kirchhoff’s 2nd Rule
Loop rule: The sum of
the changes (net
change) in electrical
potential around a
closed loop in a
circuit is equal to zero
(conservation of
energy).
Sample problem
Capacitance (Ch 17)
A capacitor consists of two conductors
that are close but not touching. A
capacitor has the ability to store electric
charge and energy.
Capacitor
• Each conductor (plate)
initially has zero net
charge
• Electrons are transferred
from one conductor to the
other (charging the
conductor)
• Equal charge magnitude
and opposite sign,
• net charge is still zero
• When a capacitor has or
stores charge Q , the
conductor with the higher
potential has charge +Q
and the other -Q if Q>0
When a capacitor is connected to a battery, the
charge on its plates is proportional to the
voltage:
(17-7)
The quantity C is called the capacitance.
Unit of capacitance: the farad (F)
1 F = 1 C/V
Examples
1. Calculate the capacitance of a parallel-plate
capacitor whose plates are 20cm x 3 cm and
are separated by a 1.0 mm air gap.
2. What is the charge on each plate if a 12.0V
battery is connected across the two plates?
3. What is the electric field between the plates?
4. Estimate the area of the plates needed to
achieve a capacitance of 1F, given the same
air gap d.
17.7 Capacitance
The capacitance does not depend on the
voltage; it is a function of the geometry and
materials of the capacitor.
For a parallel-plate capacitor:
(17-8)
17.9 Storage of Electric Energy
A charged capacitor stores electric energy;
the energy stored is equal to the work done
to charge the capacitor.
(17-10)
17.7 Capacitance
Parallel-plate capacitor connected to battery.
19.5 Circuits Containing Capacitors in
Series and in Parallel
Capacitors in
parallel have the
same voltage across
each one:
19.5 Circuits Containing Capacitors in
Series and in Parallel
In this case, the total capacitance is the sum:
(19-5)
19.5 Circuits Containing Capacitors in
Series and in Parallel
Capacitors in series have the same charge:
19.5 Circuits Containing Capacitors in
Series and in Parallel
In this case, the reciprocals of the
capacitances add to give the reciprocal of the
equivalent capacitance:
(19-6)
19.7 Electric Hazards
Even very small currents – 10 to 100 mA can
be dangerous, disrupting the nervous system.
Larger currents may also cause burns.
Household voltage can be lethal if you are wet
and in good contact with the ground.
Ammeters and Voltmeters
Voltmeter
• A voltmeter measures voltage
• It is placed in the circuit in a parallel
connection
• Measures potential difference, needs two
points on either side of component
• A voltmeter has very high resistance, and
therefore would contribute.
Ammeter
Ohmmeter
Measures Resistance.
Placed across resistor when no current
is flowing.
19.1 EMF and Terminal Voltage
Electric circuit needs battery or generator to
produce current – these are called sources of
emf.
Battery is a nearly constant voltage source, but
does have a small internal resistance, which
reduces the actual voltage from the ideal emf:
(19-1)
19.1 EMF and Terminal Voltage
This resistance behaves as though it were in
series with the emf.
Terminal Voltage and EMF
• When a current is drawn from a battery, the
voltage across its terminals drops below its
rated EMF.
• The chemical reactions in the battery cannot
supply charge fast enough to maintain the full
EMF.
• Thus the battery is said to have an internal
resistance, designated r.
• Ex: Starting a car with the headlights on, the
lights dim. The starter draws a large current
and the battery voltage drops as a result.
Terminal Voltage and EMF
• A real battery is then modeled as if it were a
perfect EMF Ɛ in series with a resistor r.
• Terminal voltage Vab
• When no current is drawn from the battery, the
terminal voltage equals the EMF.
• When a current I flows from the battery, there
is an internal drop in voltage equal to Ir, thus
the terminal voltage (actual voltage delivered)
is Vab = Ɛ - Ir
A battery whose EMF is 40V has an internal
resistance of 5 ohms. If this battery is
connected to a 15 ohm resistor R, what will
the voltage drop across R be?
1.
2.
3.
4.
5.
10 V
30 V
40 V
50V
70V
19.4 EMFs in Series and in Parallel;
Charging a Battery
EMFs in series in the same direction: total
voltage is the sum of the separate voltages
19.4 EMFs in Series and in Parallel;
Charging a Battery
EMFs in series, opposite direction: total
voltage is the difference, but the lowervoltage battery is charged.
19.4 EMFs in Series and in Parallel;
Charging a Battery
EMFs in parallel only make sense if the
voltages are the same; this arrangement can
produce more current than a single emf.