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Electric Circuits
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Definitions
Coulomb is the SI unit for an electric charge. The symbol is "C".
Electric Current ( I ) is the flow of electrons per unit time. It is
measured in coulombs per second. This measurement is also called
an ampere. Therefore 1 A = 1 C/s
Voltage (V) is electric potential energy per unit charge or
joules/coulomb such that 1 V = 1 J/C. Named after Alessandro
Volta (1745-1827).
A battery is a collection of electric cells. Each electric cell produces
a flow of electron via a chemical reaction. This is the symbol for a
battery.
Resistance is the restriction of the flow of electrons due to the
properties of the material it travels through. The symbol for
resistance is "R". The unit for resistance is called the Ohm and its
symbol is the Greek Omega
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Ohm's Law
Ohm's Law describes the relationship between current, voltage, and
resistance. Ohm's law specifically applies to electricity traveling through
metal wires.
V=IR
Resistors are devices used to control or reduce the electrical flow of
current much like a washer can be used in a water pipe to reduce the
flow of water to a shower head in order to save water.
The symbol for a resistor is
Various objects can be placed in the flow of electrical current to
produce work. The most common are lights and motors. These items
also produce a resistance much like a water wheel in a stream.
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Electric Circuits
An electric circuit is a pathway for electrical current which starts from a
battery and travels back to the same battery. There are two basic types of
electrical circuits, series circuits and parallel circuits.
SERIES CIRCUITS
In a series circuit, the resistance items are conncected one after the
other in the electrical current.
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PARALLEL CIRCUIT
In a parallel circuit, each resistance item is connected to the main flow of
electrical current.
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Advantage & Disadvantage of Series & Parallel Circuits
ADVANTAGE
The current or amperage does not
change.
SERIES
CIRCUIT
PARALLEL
CIRCUIT
DISADVANTAGE
The voltage changes after each
resistance item.
Can add more batteries to
increase power.
If one item fails, the others will not
work.
The voltage does not change after
each resistance item.
The amperage or current changes
as it passes through each device.
If one device fails, the others will
continue to work.
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Calculating the Total Equivalent Resistance
556-561
In a series circuit, the total equivalent resistance would be the sum of
all the resistance in the circuit.
Req = R1 + R2 + R3 + ....
In a parallel circuit, the following expression is used to calculate the
total equivalent resistance.
1
1
1 + 1 +
=
+
Req R1 R2 R3 ....
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Series Circuit ( voltage divider)
R1
R2
R3
Req = R1 + R2 + R3
I1 = I2 = I3
V1 = V2 = V3
V1 + V2 + V3 = VTOTAL
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Parallel Circuit ( current divider)
R1
R2
R3
I1 = I2 = I3
I1 + I2 + I3 = ITOTAL
V1 = V2 = V3
1
= 1 + 1 + 1
Req R1 R2 R3
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Problem-Solving Strategies
1) Calculate Req (Equivalent R) for the entire circuit.
2) Use Ohm's Law to find current from battery.
3) Any resisters in series with battery get IT .
4) Use Vn = ITRn for resistors in series with battery.
5) Combine series /parallel rules with V = IR for each.
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Consider the arrangement of electrical components below. The battery supplies a total voltage of 17.9 volts. The resistors are as
follows: R1 = 7.72 Ω, R2 = 21.9 Ω, and R3 = 7.50 Ω.
A. What is the equivalent resistance of R2 and R3?
B. What is the equivalent resistance of the entire circuit?
C. What is the total current in the circuit?
D. What is the voltage drop across R1?
E. What is the voltage drop across R2 and R3?
F. What is the current through R1?
G. What is the current through R2?
H. What is the current through R3?
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Consider the arrangement of electrical components below. The battery supplies a total voltage of 19.4 volts.
Fill in the voltage drops and currents through each resistor in the table. Resistance values are as shown.
R1 = 9.8Ω
R2 = 9.79Ω
R3 = 6.68Ω
R4 = 8.56Ω
R5 = 9.85Ω
R6 = 7.29Ω
First, find the total resistance of the entire circuit.
SERIES
RTotal = R123 + R45 + R6
PARALLEL
R123 = R12 + R3
R123 = (1 / (R1 + R2) + 1 / R3)-1
R45 = (1 / R4
+ 1 / R5)-1
Then, find the total current of the circuit using Ohm's Law.
Calculate the voltage drop from R6.
Now that you have the current for the entire circuit, Kirchnoff's Law says that the
current in the beginning of a circuit must equal the current at the end of the circuit.
Find the voltage for the parallel circuit.
Since it is a parallel circuit, the voltage remains the same for both sides of the parallel
circuit.
Now that we have the voltage for the parallel circuit R45, we can calculate the new
current for R4 and R5.
To find the voltage for R3, multiply the total current by R123.
To find the current I3 ...
The finial two resistors are R1 and R2 in series which means that the voltage will change but
the current will stay the same.
And since this portion of the circuit is in series...
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Consider the arrangement of electrical components below. The battery supplies a total voltage of 37.4 volts. Fill in
the voltage drops and currents through each resistor in the table. Resistance values are as shown.
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