Question

A constant voltage is applied across a circuit. If the resistance in the circuit is doubled, what is the effect on the power dissipated by the circuit?

a.The power dissipated is quadrupled

b.The power dissipated is reduced by a factor of 2.

c.The power dissipated is reduced by a factor of 4

d. The power dissipated is doubled.

e. The power dissipated remains constant.

Answer 1

b.The power dissipated is reduced by a factor of 2.

Step-by-step explanation:

The power dissipated in the circuit is given by

`P=(V^2)/(R)`

where

V is the voltage

R is the resistance

In this problem:

- The voltage V is kept constant

- The resistance is doubled, so R' = 2R

Therefore, the new power dissipated is

`P'=(V^2)/(R')=(V^2)/(2R)=(1)/(2)(V^2)/(R)=(1)/(2)P`

so, the power dissipated is reduced by a factor of 2.