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Circuit Electricity
The following symbols are used in electric circuits:
Four devices are commonly used in the laboratory to
study Ohm’s law: the battery, the voltmeter, the
ammeter and a resistance. The ammeter and voltmeter
measure current and voltage respectively.
Ammeter measures
current through the
battery, the filament,
and itself. Placed in
series
This arrangement measures
the voltage across the battery.
Placed in parallel.
Resistors are loads in a circuit. They are the
things you turn on. For labs we can insert resistors
of known resistance. They are color coded.
.
Circuits: 3 components
• Voltage Source (Battery)
• Conductor (Wire for Current to flow)
• Resistor (Load or item being “turned
on”)
2 General Types of Circuits
• Series
• Parallel
RESISTORS IN SERIES
To wire in SERIES means to make a circuit
with a single pathway for the current.
RULES FOR RESISTORS IN SERIES
Voltage Adds
VT = V1 + V2 + V3
In a series circuit, the sum of the voltage drops
equal the voltage drop across the entire circuit.
Current is constant
IT = I1 = I2 = I3
Resistance Adds
RE = R1 + R2 + R3
An equivalent resistance (RE ) is the resistance of a
single resistor that could replace all the resistors in a
circuit. The single resistor would have the same
current through it as the resistors it replaced.
Example1: Two resistances of 2 Ω and 4 Ω respectively are
connected in series. If the source of emf maintains a constant
potential difference of 12 V,
a. What is the current delivered to the external circuit?
Re = R1 + R2
=2+4
=6Ω
V 12
IT 

=2A
Re 6
b. What is the potential drop across each resistor?
V1 = I R 1
= 2(2)
=4V
V2 = I R 2
= 2(4)
=8V
Total
Voltage
Current
Resistance
1
2
RESISTORS IN PARALLEL
To wire in PARALLEL means to make a circuit
with multiple pathways for the current.
RULES FOR RESISTORS IN PARALLEL
Voltage is Constant
VT = V1 = V2 = V3
The voltage drop across each branch is equal to
the voltage of the source.
Current Adds
IT = I1 + I2 + I3
Each resistor provides a new path for electrons to
flow. The total current is the sum of the currents
through each resistor.
1
1
1
1



Reciprocals of Resistance Adds
RE R1 R2 R3
The equivalent resistance of a parallel circuit
decreases as each new resistor is added.
Example: A 5Ω and 10Ω resistor are wired in parallel
to 6V battery.
A. What is their equivalent resistance?
R1= 5Ω
R2 = 10Ω
V= 6V
1 = 1 + 1
RT
5
10
RT = 3.33 Ω
B. What is the current through each resistor?
V
I
R
= 6 V
5 Ω
V
I
R
= 0.6 A
= 6 V
10 Ω I = 1.80A
T
= 1.2 A
V
I
R
= 6 V
3.33Ω
IT= 1.80A
Total
Voltage
Current
Resistance
1
2
Why can a bird stand on
a high voltage wire and
not get shocked?
Because there is no Potential difference
between his feet.
Will either bird get shocked now?
Yes, the one over the light
bulb, because a potential
difference exists between
his feet.
A word about Electrical Safety…
If not…
Ground plugs. One end of the ground
plug is connected to the appliance
cover.
The wall jack which receives the
ground plug is connected to the ground,
so any charge leaking onto the
appliance will drain to ground not you.
You are the path of least resistance..
One milliampere: tingling sensation
Ten milliamperes: nerves and muscles overloaded
200 milliamperes: potentially fatal; heart fibrillation
500 -1000 milliamperes: not necessarily fatal; heart will
restart
One ampere or more: burn alive
As more and more appliances are
added to a circuit in parallel the
resistance decreases and the current
increases. Too much current can
result in an overload and a possible
fire.
Fuses and Circuit breakers
are used to prevent
overload, by limiting the
amount of current that can
flow through a circuit.
A fuse uses a thin metal
wire or ribbon that melts
when current through it is
too high. These must be
replaced.
Houses today use CIRCUIT BREAKERS.
These do not need to be replaced and use a
bimetallic strip that trips a switch.
Brass expands more than steel As temperature
increases, the bimetallic strip arcs to the left,
settles into groove, and the spring pulls the metal
bar down breaking the circuit.
How can we solve complex circuits?
That is circuits that have both parallel and
series components?
We will use Equivalent Resistance …
Equivalent Resistance simplifies a circuit by
replacing resistor sets with a single EQUAL
resistor…
For example:
The 8Ω and 4Ω resistors are in
series so could be replaced with
a 12Ω resistor
The 6Ω and 3Ω resistors are in
parallel. They can be replaced
with a single 2 Ω resistor.
The 12 Ω and 2 Ω resistors are
in series and could be replaced
with a single 14 Ω resistor.
Example 3: The total applied voltage to the circuit in the figure
is 12 V and the resistances R1, R2 and R3 are 4, 3 and 6 Ω
respectively.
a. Determine the equivalent resistance of the circuit.
R2 and R3 are in parallel (RP)
1 1 1
 
Rp 6 3
RP and R1 are in
series
Req = 4 + 2
= 6 Ω
Rp= 2 Ω
The total applied voltage to the circuit in the figure is 12 V and the
resistances R1, R2 and R3 are 4, 3 and 6 Ω respectively.
(b) What is the total current?
I = V/R
12V/6Ω = 2 A
(c) Find the current through and the voltage across each resistor.
R1: I = 2 A (series) so V=IR= (2 A)(4 Ω) = 8V
The remaining voltage in the circuit is 12 V – 8 V = 4
V
which means that V2 and V3 are 4 V since they are in
parallel.
I =
I2 = 4V / 3Ω 1.33 A
V/R
=
I3 = 4V / 6Ω =0.67 A
Example 3: The total applied voltage to the circuit in the figure
is 12 V and the resistances R1, R2 and R3 are 4, 3 and 6 Ω
respectively.
a. Determine the equivalent resistance of the circuit.
b. What is the total current?
c. Find the current through and the voltage across each
resistor
Total
Voltage
Current
Resistance
1
2
3