An a.c. e.m.f. of peak value $=230 \mathrm{~V}$ and frequency 50 Hz is connected to a circuit with $\mathrm{R}=11.5 \Omega, \mathrm{~L}=2.5 \mathrm{H}$ and a capacitor all in series. The value of capacitance is ' C ' for the current in the circuit to be maximum. The value of C and maximum current are respectively $\left(\pi^2=10\right)$.

The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value then its new time period will become

A simple pendulum with bob of mass m and conducting wire of length $L$ swings under gravity through an angle $\theta$. The component of earth's magnetic field in the direction perpendicular to swing is B . Maximum e.m.f. induced across the pendulum is ( $\mathrm{g}=$ acceleration due to gravity)

In a cyclic process, work done by the system is