The length of a potentiometer wire is ' $L$ ' . A cell of e.m.f. $E$ is balanced at a length $\frac{L}{5}$ from the positive end of the wire. If the length of the wire is increased by $\frac{L}{2}$, the same cell will give balance point at distance ' $x$ '. The value of ' $x$ ' is

In LCR series circuit, R = 18 $\Omega$ and impedance $33 \Omega$. An r.m.s. voltage of 220 V is applied across the circuit. The true power consumed in a.c. circuit is

A child stands on a weighing machine inside a lift. When the lift is going down with acceleration $\mathrm{g} / 3$, the machine shows a reading 20 N . When the lift goes upwards with acceleration $\mathrm{g} / 3$, the reading would be ( $\mathrm{g}=$ gravitational acceleration)

The equivalent capacitance between plates ' A ' and ' B ' ( A -area of each plate, d-separation between plates) ( $\varepsilon_0$ - permittivity of free space) is