In an a.c. circuit containing $L, C, R$ in series the ratio of true power to apparent power is ( $\mathrm{Z}=$ impedance of the circuit and R is the resistance)

Two wires of equal lengths are bent in the form of a square and a circular loop. They are suspended in a uniform magnetic field and same current is passed through them. Torque experienced by

A calorimeter contains 10 g of water at $20^{\circ} \mathrm{C}$. The temperature fall to $15^{\circ} \mathrm{C}$ in 10 min . When calorimeter contains 20 g of water at $20^{\circ} \mathrm{C}$, it takes 15 min . for the temperature to become $15^{\circ} \mathrm{C}$. The water equivalent at the calorimeter is

Under isothermal conditions, two soap bubbles of radii $r_1$ and $r_2$ coalesce to form a big drop. The radius of the big drop is