Chapter 24, Problem 80GP

Predict/Calculate When a certain resistor is connected to an ac generator with a maximum voltage of 15 V, the average power dissipated in the resistor is 22 W. (a) What is the resistance of the resistor? (b) What is the rms current in the circuit? (c) We know that $P_{\text{av}}=I_{\text{rms}}^{2}R$, and hence It seems that reducing the resistance should reduce the average power. On the other hand, we also know that $P_{av}=V_{rms}^2/R$, which suggests that reducing R increases p_av. Which conclusion is correct? Explain.