Parallel Circuits

Parallel CircuitsI

_

+V R R

I1 I2

I

Parallel Circuit RulesA parallel circuit has two or more paths

for current to flow through.

Voltage is the same across each component of the parallel circuit.

VVSS = V = V11 = V = V22 = V = V33…  … 

Parallel Circuit RulesThe sum of the currents through each path is equal to the total current that

flows from the source. 

IITT = I = I11 + I + I22 + I + I33……

Let’s find the total Resistance

IITT = I = I11 + I + I22 + I + I33……

Use V and R to find I:

VVTT V V11 V V22 V V33

RRTT R R11 R R22 R R33== ++ ++

VVTT V V11 V V22 V V33

RRTT R R11 R R22 R R33== ++ ++

Use: VUse: VSS = V = V11 = V = V22 = V = V33     1 1 1 11 1 1 1

RRTT R R11 R R22 R R33== ++ ++

Parallel Circuit Rules

The Total Resistance of a Parallel Circuit is always less

than the smallest resistor. 

Example

IT

IT_

+V R1 R2

I1 I2

R3

I3

ExampleGiven: V = 36V R1 = 6 Ω

R2 = 9 Ω R3 = 18 Ω

Find: RT = ? I1 = ?

I2 = ?I3 = ?

Example

IT

IT_

+V R1 R2

I1 I2

R3

I3

ExampleGiven: V = 120V R1 = 30k Ω

R2 = 30k Ω R3 = 30k Ω

Find: RT = ? I1 = ?

I2 = ?I3 = ?

Comp

123

Total

RkΩ ImA VV PmW

30303010 120

1201201204

44

12

4804804801440

Example

IT

IT_

+V R1 R2

I1 I2

R3

I3

ExampleGiven: R1 = 6Ω IT = 10mA

I2 = 3mA I3 = 2mA

Find: RT = ? VT = ?

II = ?R2 = ? R3 = ?

Comp

123

Total

RkΩ ImA VV PmW

610153 30

30 30305

32

10

1509060300