Parallel Circuits – Chapter 5

• A parallel circuit provides more than one current path between any two points.

• Each current path in a parallel circuit is referred to as a branch.

Two Branches Three Branches

How many branches?

Parallel Circuit Characteristics

Voltage and Current Values

Voltage is the same across all components

(a) No parallel branches (b) V1 = V2 = VS

Parallel Circuit Characteristics

Current Characteristics Source current is the sum of all branch currents

nT IIII ...21

whereIn = the current through the nth branch in

the circuit

The total current in the circuit is IT = I1 + I2 + I3

IT = 5mA + 10mA + 20mA = 35mA

Parallel Circuit Characteristics

Voltage and Current Values Current through each branch is determined by the source voltage

and the resistance of the branch.

Sbranch

branch

VI

R

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Use Ohm’s law to calculate the resistance in each branch.

TEAM ACTIVITY

1

102000

0 005R

.

2

101000

0 010R

.

3

10500

0 020R

.

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Use Ohm’s law to calculate the total resistance.

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10285 71

0 035TR ..

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1

102000

0 005R

.

2

101000

0 010R

.

3

10500

0 020R

.

10285 71

0 035TR ..

Calculate1 2 3

1 1 1

R R R

1

TR

Summary

1 2 3

1 1 1 1

TR R R R

1 2 3 TI I I I

1 2 3 SV V V V

1 2 3

11 1 1 TR

R R R

Common Mistake

1 2 3

1 1 1 1

TR R R R 1 2 3 T

Series Circuit

R R R R

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1P

2P

3P

TP

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1 0 05P . W

2 0 1P . W3 0 2P . W

0 35TP . W

1 2 3TP P P P

Special Case – Equal Resistances

• When any number of equal resistances are connected in parallel, the total resistance is equal to the value of one resistor divided by the number of branches

Shorthand notation for parallel

Special Case – Equal Resistances

Shorthand notation for parallel

1 1 1 1 3

TR R R R R

5 11 7

3 3T

R . kR . k

Adding Additional Branches

• The addition of a parallel branch decreases the resistance of the circuit

• single branch in (a) draws 5mA from the source• additional branch in (b) increases the current

drawn from the source to 10mA

Vs8 V

R11kOhm

R2200 Ohm

Vs12 V

R11.5kOhm

R23kOhm

Determine the branch currents and the total current for each circuit. Check with MultiSim.

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