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Physics: Introduction to Electrical Circuits
Notes and Problems Packet for Chapters 20, 22, 23
Chapter 20: Static Electricity
Summary:
20.1
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20.2
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There are two kinds of electrical charge, positive and negative. Like charges repel;
unlike charges attract.
Electrical charge is not created or destroyed. It is conserved.
Objects can be charged by the transfer of electrons.
Charges added to one part of an insulator remain on that part.
Charges added to a conductor quickly spread over the surface of the object.
When an electroscope is charged, electrical forces cause its thin metal leaves to
spread apart.
An object can be charged in 3 ways:
o Friction: rubbing two objects together causes charge to separate.
o Contact: by touching a charged object to it
o Induction: a charged object is first brought nearby, causing a separation of
charges. Then the object to be charged is separated, trapping opposite charges
on the two halves.
The SI standard unit of charge is the coulomb (C). One coulomb is the charge of 6.25
x 1018 electrons or protons. The elementary charge, the charge of the proton or
electron, is 1.60 x 10–19 C.
 Coulomb’s Law:
The force between two charges varies directly with the product of their charge and
inversely with the square of the distance between them.
(the format is identical to Newton’s Law of Universal Gravitation):
F = K qA qB
d2
where F is the force between the charges
K is the constant, 9.0 x 10 9 N  m2 / C2
qA is charge A
qB is charge B
d is the distance separating the two charges
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Problem set 1:
1.1 A strong lightning bolt transfers about 25 C to Earth. How many electrons are
transferred?
1.2 A positive and a negative charge, each of magnitude 1.5 x 10 –5 C, are separated by a
distance of 15 cm. Find the force on each of the particles.
1.3 How far apart are two electrons if they exert a force of repulsion of 1.0 N on each other?
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Chapter 22: Current Electricity
Electric Current: A flow of charged particles is an electric current. Charges flow from a
higher potential to a lower potential. A common source of continuous potential difference is
the battery, a charge pump.
Electric Circuits: Charge will move through a closed loop from a charge pump via a
conductor (e.g., a wire) from one end of the pump and back again. Such a closed loop is
called an electric circuit.
A circuit includes
 a charge pump, which increases the potential energy of the charges moving from A
to B; for example, a battery or a generator
 a device that reduces the potential energy of the charges moving from B to A, the
load. The potential energy lost by the charges in moving through a load (e.g., a
motor, a lamp, a doorbell). This potential difference is called V or, more
commonly, V.
Conservation of charge: Like energy, charge can neither be created nor destroyed, only
separated. Thus, the total amount of charge in a circuit (number of negative electrons and
positive ions) does not change.
Energy is conserved. The potential difference created by the charge pump (e.g., battery,
generator) equals the potential difference decrease across the load.
Power:
Power measures the rate at which energy is transferred. Since the unit used
for quantity of electric charge is the coulomb, thus, the rate of flow of electric charge is
electric current, I. It is measured in amperes (or amps, for short), (the symbol for ampere is
A). A flow of one coulomb per second equals one ampere.
1 C/s = 1 A
A device that measures electric current is called an ammeter.
Power is represented by the following equation:
P = IV
Where P = power, measured in watts, W
I = electric current, measured in amps, A
V= electric potential difference, measured in volts
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Problem Set II:
2.1. The current through a lightbulb connected across the terminals of a 120-V outlet is 0.50
A. At what rate does the bulb convert electric energy to light.
2.2. What is the current through a 75-W lightbulb connected to a 120-V outlet?
2.3 (This one is harder) The current through the starter motor of a car is 210 A. If the
battery keeps 12 V across the motor, what electric energy is delivered to the starter in
10.0 s? [Hint: once you have calculated the power, then remember that power is in watts
which is the same as Joules per sec. And Joules is the unit of Energy which is what you
are being asked to find]
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OHMS’s LAW:
V = IR
where V is the potential difference (measured in volts, V)
I is the electric current (measured in amps, A)
R is the resistance (measured in ohms, )
Resistance is a variable defined as: one ohm (--this is the Greek letter omega) is the
resistance that permits a current of 1 A to flow when a potential difference of 1 V is applied.
Problem Set III:
3.1
An automobile headlight with a resistance of 30  is placed across a 12-V battery.
What is the current through the circuit?
3.2 A motor with an operating resistance of 32  is connected to a voltage source. The
current in the circuit is 3.8 A. What is the voltage of the source?
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3.3 A lamp draws a current of 0.50 A when it is connected to a 120-V source.
a. What is the resistance of the lamp?
b. What is the power consumption of the lamp?
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Chapter 23: Series and Parallel Circuits
Diagramming Circuits:
The following symbols are commonly used in circuit diagrams.
Draw they symbols next to the terms below:
{See bottom of page 515 for the symbols}
Conductor
Open:
Switch
Electric
Connection
Closed:
Fuse
No Electric
Connection
Capacitor
Battery
(indicate
+ and –
terminals)
Resistor
(fixed)
Lamp
Potentiometer
(variable resistor)
DC Generator
Inductor
Voltmeter
Ground
Ammeter
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Steps to follow when diagramming circuits:
(Always diagram in right angles. No loops or curves: it is a diagram, not a drawing.)
1. Draw the symbol for the battery or other source of electric energy (such as a
generator) at the left side of the page. Put the positive terminal on top.
2. Using a ruler or straightedge, draw a wire coming out of the positive terminal. When
you reach a resistor or other device, draw the symbol for it.
3. If you reach a point where there are two current paths, such as at a voltmeter, draw a
.
in the diagram.
4. Follow one path until the two current paths join again. Then draw the second path.
5. Follow the current path around the diagram, always changing direction at right
angles, using straight lines until you reach the negative terminal of the battery.
6. Check your work to make sure that you have included all parts and that there are
complete paths for current to follow. Remember, electric current will flow only if
there is a complete circuit!
A word about a couple of important measuring devices:
Ammeter
Measures current through a circuit component. The same current that goes through
the component must go through the ammeter, so there can be only one current path. This
connection is called a series connection. To add an ammeter to a circuit, you must remove
the wire connected to the circuit component and connect it to the ammeter instead. Then
connect another wire from the second terminal of the ammeter to the circuit component.
Always associate the words current through.
Voltmeter
Measures potential difference across any component of a circuit. When connecting
the voltmeter in a circuit, connect the + terminal to the end of the circuit component closer to
the + (positive) terminal of the battery and connect the other terminal to the other side of the
component. This kind of connection is called a parallel connection because the circuit
component and the voltmeter are aligned parallel to each other in the circuit. The potential
difference across the voltmemter is equal to that across the circuit element. Always associate
the words voltage across.
The convention for the direction of current flow: it is the direction in which a positive charge
would move. Of course, we know that it is the negative charge that is moving. They didn’t
know that when the convention was established.
Problem Set IV:
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4.1
Draw a circuit diagram to include a 60-V battery, an ammeter, and a resistance of
12.5  in series. Indicate the ammeter reading and the direction of current.
4.2
Draw a series-circuit diagram showing a 4.5-V battery, a resistor, and an ammeter
reading 90 mA. Label the size of the resistor. Choose a direction for the
conventional current and indicate the positive terminal of the battery.
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Chapter 23: Series and Parallel Circuits
23.1 Simple Circuits:
Series Circuits:
A series circuit is a circuit in which current passes through each device, one after another.
Devices are connected head-to-tail.
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The current (I) is the same everywhere. It makes sense: since the current is the flow
of electrons, they will be flowing the same rate everywhere along a series circuit.
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The equivalent resistance (R) is the sum of the resistances of its parts. That is,
R = R1 + R2 + R3 + …
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The total potential difference (V) is the sum of the voltage drops across each of the
resistors. That is,
V = V1 + V2 + V3 + …
Series Circuit Activity:
(1) Draw a Series Circuit below with one battery and 3 loads of various resistance, R1, R2, R3.
Label the resistors and voltage drops across each resistor, V1 , V2, V3. If the resistors were 1,
2 and 3 ohms respectively and the total current flowing in the circuit is 2 Amps, (2) what is
the total potential difference in the circuit and (3) what are the values for V1, V2, V3?
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Parallel Circuits:
A parallel circuit is a circuit with several current paths.
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The total current (I) is equal to the sum of the currents in the branches.
I = I1 + I2 + I3 + …
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The reciprocal of the equivalent resistance (1/R) is equal to the sum of the
reciprocals of the individual resistances.
1
=
R
1
R1
+
1
R2
+
1
+
…
R3
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The total potential difference (V) is the same across each of the branches of the
parallel circuit.
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If any branch of a parallel circuit is opened, there is no current in that branch. The
current in the other branches is unchanged.
Parallel Circuit Activity:
Using the same data for the Series Circuit activity above, (1) construct a parallel circuit with
the three resistances, R1, R2, R3. of 1,2, and 3 ohms, respectively, in parallel with each other.
The total potential difference across the circuit is 120 Volts. (2) What is the equivalent
resistance of the circuit? (3) How much total current is flowing in the circuit?
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23.2
On page
9, add a voltmeter to each circuit that measures the potential difference across the
resistors in the circuit diagrams 4.1 and 4.2.
23.2 Applications of Circuits
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A fuse or circuit breaker, placed in series with appliances, creates an open circuit
when dangerously high currents flow.
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A complex circuit is often a combination of series and parallel branches. Any
parallel branch is first reduced to a single equivalent resistance. Then any resistors in
series are replaced by a single resistance.
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An ammeter is used to measure the current in a branch or part of a circuit. An
ammeter always has a low resistance and is connected in series.
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A voltmeter measures the potential difference (voltage) across any part or
combination of parts of a circuit. A voltmeter always has a high resistance and is
connected in parallel with the part of the circuit being measured.
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A short circuit is a low resistance connection between two points.
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