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Electric Circuits
Electric circuits transfer energy. Electrical energy is converted into light, heat, sound,
mechanical work, etc. The by product of any circuit is always heat.
DC current (direct current)
a steady flow of current in one direction
AC current (alternating current)
direction of current flow changes many times a second. In the US, the frequency
of change is 60 Hz. Therefore, the current changes direction 120 times per second.
emf (electromotive force)
source of energy moving electrons through the circuit. For a battery, the
maximum potential difference that exists between the terminals is referred to as
the emf () of the battery.
electric current (symbol is I; SI unit is the ampere, or A)
flow of charge, or current = charge/sec
1 A = 1 C/ sec
Consider a circuit composed of wire connecting the terminals of a battery. Within
the battery, a chemical reaction occurs that transfers electrons from one terminal
to another. Because of the positive and negative charges existing on the battery
terminals, a potential difference (voltage) exists between them. The battery
creates an electric field within and parallel to the wire, directed from the positive
toward the negative terminal. This field exerts a force on the free electrons,
causing them to move. This movement of charge is known as an electric current.
The current is how much charge flows in a unit of time,
I = q /t
conventional current
flow of positive charge
electric power (symbol is P; SI unit is watt)
the rate of doing electrical work. The amount of energy per unit of time (power) is
the amount of charge, q, that comes from the battery in a time t across a
potential difference V. Or, P = (q / t) V. Since q / t is the current I, power is
the product of current and voltage.
P = VI = (IR)I
P = I2R = V2/R
Watt
SI unit of power; 1 Watt = 1 Joule/sec = 1 VoltAmp
electrical energy (symbol is EE; SI unit is Joule)
EE = P t
EE = V I t
Total power The total power in a series combination of light bulbs and in a
parallel combination of light bulbs is simply the sum of the individual wattages.
For example, two 60 W light bulbs have to dissipate 120 W in a series
combination as well as in a parallel combination.
Electric companies sell you electrical energy. Your energy consumption is
computed by expressing power in kilowatts and time in hours. Energy is sold to
you in units of kW-hr.
AP Multiple Choice & Free Response Questions on Electrical Energy:
1. They like to ask questions about heaters! They will tell you the wattage of
a heater. Remember this is the unit of power (P=Vi). They will ask how
much energy the heater will use in a certain amount of time (Remember electrical energy=Vit).
2. As part of a free response question, they will give you the wattage of a
heater and ask you how much thermal energy it dissipates in a certain
amount of time.
3. They will ask you to calculate how much the electrical energy costs to
operate a device of known current and voltage for a known amount of
time.
resistance (symbol is R,; SI unit is ohm or )
opposition to current flow
1  = 1 V/ 1 A
Ohm’s law
for a given resistance, the potential difference is proportional to the current flow
V=IR
The current that a battery pushes through a wire can be compared to the flow of water
that a pump pushes through a pipe. Greater pump pressures cause greater water flow
rates; greater voltages cause greater currents. In a pipe, other things determine the water
flow rate besides just the pump pressure; in a circuit, other things determine the current
magnitude besides just the voltage. Longer and narrower pipes cause greater resistance to
the water flow; longer and smaller diameter wires cause greater resistance to the current.
Resistance of a solid conductor depends upon:
1.
2.
3.
4.
nature of the material
length of the conductor
cross-sectional area of the conductor
temperature
.
Resistivity Resistivity is an inherent property of a material. Its unit is  meter. Its
symbol is . Insulators have large resistivities; conductors have small resistivities.
Semiconductors, such as germanium and silicon, have intermediate resistivities. The
resistivity also depends upon temperature. In metals, the resistivity increases with
increasing temperature; in semiconductors, the reverse is true.
 = o[1 + (T - To)]
where  is the temperature coefficient of resistivity, T and To are the temperature
and initial temperature, respectively.
Resistance and resistivity The resistance, R, of a material of length, L, and
cross-sectional area, A, is given by
R=L/A
AP Multiple Choice Questions on Resistivity:
They will give you five pictures of wires. They may vary by length, crosssectional area, or be tapered (one end's cross-sectional area is bigger than
the other end's). They will ask you which wire has the greatest or the least
resistance.
1. They will give a picture of two wires with different cross-sectional areas
and ask you by how much one wire's cross-sectional area differs from an
others (another example of how they love ratios!).
Critical Temperature. The temperature below which the resistivity of a class of
materials goes to zero. Below this temperature, such materials are called
superconductors. Since these materials have zero resistivity below the critical
temperature, they offer no resistance to electric current. Once a current is
established in a superconducting material below its critical temperature, it
continues indefinitely with no need of an outside voltage source. Metals are
superconducting at temperatures slightly above absolute zero. Some ceramics
have been developed with critical temperatures as high as 133.5 K.
Terminal voltage (Vab) When using a battery, what is really measured is the
voltage delivered to the circuit, or the voltage between the two terminals. When
no current is drawn from the battery, the terminal voltage is equal to the emf .
When a current is drawn, the voltage between the terminals is called the terminal
voltage, the actual voltage delivered to the circuit.
Internal resistance (r)When a current is drawn from a battery, over time, the
voltage delivered to the circuit by the battery drops below its listed emf. A battery
itself has some internal resistance due to the chemical reactions moving charges
from one terminal to another.
Vab =  - Ir
AP Free Response Questions about Internal Resistance:
1. You may be given a battery in a circuit that contains an internal resistance.
They may ask you to calculate the voltage delivered to the circuit.
2. They will duplicate an experimental situation for a circuit consisting of a
variable resistor and a battery with internal resistance. You are given data
terminal voltage vs. current data as the resistance is varied. From this
information, you will be expected to calculate the emf and the internal
resistance of the battery.
Experimentally determine the relationship between current, voltage, and
resistance http://jersey.uoregon.edu/vlab/Voltage/index.html
galvanometer
Measures small currents
ammeter
Measures current
Ammeters and galvanometers are connected in a circuit, positive to positive and
negative to negative; they have very low resistance so that the current flow
through them is a maximum; they are connected in series
voltmeter
Measures potential difference between two points in a circuit
Voltmeters are connected in a circuit, positive to negative and negative to
positive. They have very high resistance so that the current flow through them is a
minimum; they are connected in parallel
Circuit symbols
AP Free Response Questions on Meters:
1. You will be asked to draw the correct placement for an ammeter and a
voltmeter in a circuit.
2. You will be given meters and other equipment. You must design an
experiment that will take the appropriate current and voltage readings to
calculate resistance. Usually, these are related to ultimately determining a
temperature.
Series Circuits
Series circuit
Resistors are connected so that there is only one path for the current to flow
through the resistors; the current is the same at all points - current is constant in
series
Effective resistance (equivalent resistance)
the resistance of a single resistor that could replace all the resistors in a series
circuit
Kirchoff’s second law
in any closed circuit loop, the potential energy drops of the individual electrical
devices equals the total energy of the circuit; this is a statement of the law of
conservation of energy
As resistors are added in series, total resistance increases and total current
decreases.
Steps in simplifying series circuits:
1. find the effective resistance of the circuit
2. find the total current using Ohm’s law
3. apply Ohm’s law to each individual resistor to determine the individual
resistor’s voltage drop
Parallel Circuits
Parallel circuits
Resistors in parallel have the same voltage drop across them. The sum of the
currents in each parallel branch equals the total current entering the parallel
branch of resistors. Voltage is constant in parallel.
Kirchoff’s first law
The sum of the currents entering a point is equal to that of the currents leaving the
point.
In a parallel circuit, all the resistors in parallel can be replaced with one
equivalent resistance that carries the same current and has the same voltage drop
across it.
As resistors are added in parallel, total resistance decreases and total current
increases.
Power companies maintain a house voltage of 120 V. House appliances are
connected in parallel. The more appliances on a circuit, the lower the total
resistance, the greater the current. Fuses protect against circuit overloading.
Steps in simplifying parallel circuits:
1. find the equivalent resistance
2. use Ohm’s law to find total current
3. apply Ohm’s law to each resistor to find the current in that branch
Complex Circuits
Complex circuits are a combination of resistors in parallel and in series.
steps in simplifying complex circuits:
1.
2.
3.
4.
5.
determine the equivalent resistance of each set of resistors in parallel
determine the total resistance of the circuit
determine total current
calculate voltage drops across all series resistors
calculate currents in each parallel branch
AP Multiple Choice Questions
1. This is a big percentage of the AP test!
2. They will give you diagrams of two resistors arranged in series or in
parallel. Then they will give you the same diagrams, but the resistors will
be double what they were. They will ask you which combination of
resistors yields the largest or the smallest equivalent resistance.
3. They will give you a diagram showing a complex circuit consisting of a
resistor in series with two or more resistors in parallel and ask you the
potential difference across one of the parallel resistors.
4. They will give you a diagram of two resistors in parallel and ask you what
happens to the current (or certain ammeter reading) or voltage (or certain
voltmeter reading) when another equivalent resistor is added in parallel.
5. They will give you diagrams of two or more resistors &/or a capacitor
arranged in series, in parallel, or in a complex network and ask you which
circuit will store more energy or dissipate the most power (Remember,
since P=Vi the circuit with the greatest possible combination of voltage
and current will dissipate the most power. Remember, since stored
energy=1/2 qV, the circuit which stores the most energy has the greatest
voltage with the greatest charge stored on its plates.).
6. They may ask you to calculate the equivalent resistance between two
points in a circuit.
7. In a circuit consisting of at least one unknown resistor, you may be asked
to calculate the value of the resistance that would yield a specific current
at a known voltage.
8. You need to know what units are equivalent to. In other words, what is a
Watt equivalent to? What is a Joule equivalent to?
AP Free Response Questions
1. They like to give you various objects to put into circuit. You will be
required to draw the circuit diagram. You might be required to construct a
circuit using all the objects in which the current is as large or as small as
possible. Or, one in which the circuit will have a prescribed function.
2. One of your objects could be a variable resistor. You will be asked to
determine its resistance in the circuit as you have drawn it.
3. Predict how the brightness of a circuit containing a light bulb will change
if a variable resistor's resistance is increased or decreased. Predict how the
power dissipated in another object would change if the variable resistor's
resistance is increased or decreased.
4. You may be given a circuit diagram of a complex circuit and asked to
calculate a specific current or voltage. You may be asked to calculate
equivalent resistance, circuit current, or the power dissipated in the circuit.
5. You may be given a circuit with several light bulbs and asked how the
brightness of the bulbs would changed by screwing in or unscrewing
specific light bulbs. Remember, treat the light bulbs as if they were a
resistor (if nothing else, assign them a resistance of say 5 ohms each!).
Calculate the current through each part of the circuit for each situation
described. The brightness of the bulb is directly related to the current.
Kirchoff's Laws Circuits
Some circuits cannot be analyzed using the above methods. They might contain
multiple voltage sources or have arrangements of resistors too complex for
analysis using the above methods. They are best using Kirchoff's point rule and
loop rule.
Point (or junction) rule The total current directed into a point (or junction) must
equal the total current directed out of the point( or junction).
Loop rule For a closed loop, the total of all the potential rises is the same as the
total of all the potential drops.
Steps used to analyze a circuit using Kirchoff's laws:
1. Draw the direction of the currents in each branch. The direction is
arbitrary. If you have chosen the wrong direction, your current will turn
2.
3.
4.
5.
6.
7.
8.
9.
out negative in your solution. (Remember, currents must enter and leave
the point (or junction). They can't all enter or all leave.)
Choose an arbitrary direction in which to traverse the loops of your circuit.
(They must either be traversed all in a clockwise or all in a
counterclockwise direction.)
If you traverse a resistor in the direction of the designated current flow, it
is a voltage drop. The amount of the voltage drop is given by -iR.
If you traverse a resistor opposite the direction of the designated current
flow, it is a voltage rise. The amount of the voltage rise is given by +iR.
If you traverse an emf in the direction of the emf (conventional current is
+ to -), it is a voltage rise, or +
If you traverse an emf opposite the direction of the emf (conventional
current is + to -), it is a voltage drop, or -
To analyze you circuit, apply the point (or junction) rule. You will write
an equation showing the currents that enter and leave a point. (For
example, if there are three currents that share a common point, you can
specify that two enter and one leaves. Or, i1 + i2 = i3)
To analyze your circuit, apply the loop rule. Starting at a point, traverse
each closed loop in the designated direction, adding the voltage rises and
drops. This sum of rises and drops equals zero. You need to write one less
loop equation than you have unknown currents. In other words, if you
have three unknown currents, you need to write two loop equations.
Algebraically solve your equations for the unknown currents. (Or, you
may use a graphing calculator to do so. On the TI-86 or TI-85, you may
use the simultaneous equation feature. On the TI-83, you may use the
matrix feature.)
AP Free Response Questions on Kirchoff Law Circuits:
1. You may be given a circuit diagram containing more than one voltage
source. The calculations that they ask require your being able to calculate
the currents through the branches of the circuit.