# Series and Parallel Circuits ```Principles of Physics

Figure 3

R1
R2


More than one resistor in
multiple paths
Electrons may go through any
path
More electrons will go through
path with less resistance
Overall resistance goes down
because more than one
electron can get through at
once
One connection
between resistors
Two connections
between resistors

Figure 3
R1
R2


Current flow is different in each
path depending on the
individual resistance
I1 = V1/R1
Total current (current leaving or
entering the voltage supply)
depends on total resistance
IT = VT/RT
Current in all paths add up to
the total current leaving the
supply
IT = I1 + I2 + …

Figure 3
R1
R2

Voltage gained by electrons
when leaving the voltage
supply equals the voltage
lost before returning
Since each electron takes a
separate path it must lose all
of its voltage through the
resistor in that path
VT = V 1 = V 2 = …
Figure 3
R1
R2
To determine the current leaving
the voltage supply the total
resistance must be used
1
RT = 1 + 1 + …
R1
R2
Determine the total resistance in the
circuit at left if R1 = 6 Ω and R2 = 6 Ω
Figure 3
R1
R2
RT =
RT =
RT =
1
1 + 1
R1
R2
1
1 + 1
6
6
1
0.167 + 0.167
RT = 3 Ω
=
1
0.333
Figure 3
12 V
4Ω
4Ω
Determine the total resistance of the
circuit.
1
RT = 1 + 1
R1
R2
1
RT = 1 + 1
4
4
1
1
RT = 0. 25 + 0.25 =
0.5
RT =
2Ω
Determine the total current
of the circuit.
Figure 3
12 V
4Ω
4Ω
V = IR
12 = I(2)
I=6A
Determine the current
through each of the
resistors
Figure 3
12 V
4Ω
4Ω
V = IR
12 = I(4 )
I=3A

Adding a resistor in parallel decreases the
overall resistance



Total resistance will be less than any of the
individual resistors
When one resistor is disconnected only that
path is open – current flows in the rest of the
circuit (light bulbs will stay lit)
Everyone picks one door to get out

Most will go through largest door
```