A resistor of $50 \Omega$, inductor of self inductance $\left(\frac{3}{\pi^2}\right) \mathrm{H}$ and a capacitor of unknown capacity are connected in series to an a.c. source of 100 V and 50 Hz . When the voltage and current are in phase, the value of capacitance is (nearly)

A monoatomic ideal gas, initially at temperature $T_1$ is enclosed in a cylinder fitted with frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. $L_1$ and $L_2$ are the lengths of the gas columns before and after the expansion respectively. The ratio $T_2 / T_1$ is

Charges of $2 \mu \mathrm{C}$ and $-3 \mu \mathrm{C}$ are placed at two points A and B separated by 1 m . The distance of the point from A , where net potential is zero, is

For detecting light intensity we use