In the potentiometer circuit shown, the galvanometer shows no deflection for $AD=35 \mathrm{cm}$. The resistance of wire $AB$ is $18 \mathrm{\Omega }$ And its length is $50 \mathrm{cm}$. Calculate the emf $E$ Of the cell.

The power consumption by the circuit shown in figure at steady state is

   A cell of emf $E$ and internal resistance $r$ is connected to a variable external resistance. The figure shows the terminal voltage of cell with current in the circuit. The maximum power that can be delivered to the external resistance is

A part of a circuit is shown in the figure in steady state. The energy stored in the capacitor is

A large network is made of regular hexagonal units as shown in figure. If resistance of each straight section is $r$, then equivalent resistance of network between the points $A$ and $B$ is

Two spherical conducting shells of radii $R$ and $2R$ is filled with material of resistivity $\rho$. The strength of electric field at $r=\frac{3R}{2}$ from centre when a battery is connected as shown, is

During an experiment with a metre bridge, the galvanometer shows a null point when the jockey is pressed at $40.0 \mathrm{cm }$using a standard resistance of $90\mathrm{ }\mathrm{\Omega }$ ,as shown in the figure. The least count of the scale used in the metre bridge is $1\mathrm{mm}$. The unknown resistance is

A rod of length $l$ has varying cross-section as shown in figure. The resistivity of material is $\rho$. If potential difference across two ends is $V$, then current through the rod is