In a given circuit, the instantaneous values of the alternating voltage and current are $V=0.5 \sin \left(80 \pi t+\frac{\pi}{3}\right)$ volt and $I=0.5 \sin (80 \pi t)$ ampere respectively. Find the average power consumed in that circuit.

An electronic device operates at 2 MHz . The oscillating circuit has an inductance $20 \times 10^{-5} \mathrm{H}$. What is the capacitive reactance of the resonant circuit?

An AC generator having 400 turns and an area of cross section of $2 \times 10^{-3} \mathrm{~m}^2$ rotates with an angular speed of $200 \pi \mathrm{rad} \mathrm{s}^{-1}$ in a uniform magnetic field of strength 0.4 T . The generator is connected to the primary of an ideal transformer having 500 turns in the primary and 2000 turns in the secondary. The secondary is connected to a $400 \Omega$ resistive load. What is the rms current in the secondary of the transformer? Assume, the transformer is ideal and the resistance of the coil is negligible

A solenoid having resistance $R=60 \Omega$ and inductance $L=0.4 \mathrm{H}$ is connected to an AC source $V=100 \sqrt{2} \sin 200 t$.

Find the maximum current.