Answer:
d) The average power increases by a factor of 9 because it is proportional to the square of the rms voltage.
Explanation:
The average power dissipated in an ac circuit containing only one resistor is given by
[tex]P=\frac{V_{rms}^2}{R}[/tex]
where
[tex]V_{rms}[/tex] 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
[tex]V_{rms}'=3 V_{rms}[/tex]
so the new power dissipated will be
[tex]P'=\frac{(3 V_{rms}^2}{R}=9\frac{V_{rms}^2}{R}=9P[/tex]
So, the power dissipated increases by a factor 9.
