Question

The average power dissipated in a resistor when an AC current of peak value i_m flows through it is ______.

Options

• P = \[i_m^2R\]

• P = \[\frac{1}{2}i_m^2R\]

• P = 2\[i_m^2\]R

• P = 0

Answer 1

The average power dissipated in a resistor when an AC current of peak value i_m flows through it is P = \[\frac{1}{2}i_m^2R\].

Explanation:

The instantaneous power is p = \[i_m^2R\sin^2\omega t\]. Averaging over a full cycle using (sin^⁡2ωt) = \[\frac {1}{2}\] gives P = \[\frac{1}{2}i_m^2R\]​ = I²R, where (I) is the rms current. Power dissipation is always positive regardless of current direction.