Question

1. A circuit contains an ac generator and a resistor. What happens to the average power dissipated in the resistor when the frequency is doubled and the rms voltage is tripled? (a) Nothing happens, because the aver- age power does not depend on either the frequency or the rms voltage. (b) The average power doubles because it is proportional to the frequency. (c) The average power triples because it is proportional to the rms volt- age. (d) The average power increases by a factor of 32 5 9 because it is proportional to the square of the rms voltage. (e) The average power increases by a factor of 2 3 3 5 6 because it is proportional to the product of the frequency and the rms voltage.

Answer 1

d) The average power increases by a factor of 9 because it is proportional to the square of the rms voltage.

Step-by-step explanation:

The average power dissipated in an ac circuit containing only one resistor is given by

`P=(V_(rms)^2)/(R)`

where

`V_(rms)` is the rms voltage

R is the resistance of the resistor

As we can see, the average power dissipated depends quadratically on the rms voltage, but it does not depend on the frequency.

In this problem, the rms voltage is tripled, so

`V_(rms)'=3 V_(rms)`

so the new power dissipated will be

`P'=((3 V_(rms)^2)/(R)=9(V_(rms)^2)/(R)=9P`

So, the power dissipated increases by a factor 9.