Everything Science Grade 10

CHAPTER 17. ELECTRIC CIRCUITS 17.5

Adding a resistor to the circuit in

parallel decreases the total resistance

V = 2 V

R = 2Ω

A I = 1 A

V = 2 V

R = 2Ω

A I = 3 A

R = 1Ω

A

A

I = 1 A

I = 2 A

The currentis bigger

The total resistance of a number of parallel resistors is NOT the sum of the individual
resistances as the overall resistance decreases with more paths for the current. The total
resistance for parallel resistors is given by:

1

RP =

1

R 1 +

1

R 2 +...

Let us consider the case where we have two resistors in parallel and work out what the final
resistance would be. This situation is shown in the diagram below:

b

b

R 2 R 1

Applying the formula for the total resistance we have:

1

RP =

1

R 1 +

1

R 2 +...

There are only two resistors

1

RP =

1

R 1 +

1

R 2

Add the fractions

1

RP =

1

R 1 ×

R 2

R 2 +

1

R 2 ×

R 1

R 1

1

RP =

R 2

R 1 R 2 +

R 1

R 1 R 2

Physics: Electricity and Magnetism 303