In the circuit element given here,if the potential at point $B$,$V_B = 0$,then the potentials of $A$ and $D$ are given as

The force acting on a body moving along the $x-$axis varies with the position of the particle as shown in the figure. The body is in stable equilibrium at

Two cylinders $A$ and $B$ fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 ~K$. The piston of $A$ is free to move while that of $B$ is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 ~K$, the rise in temperature of the gas in $B$ is (in $~K$)

Two cells $E_1$ and $E_2$ having equal e.m.f '$E$' and internal resistances $r_1$ and $r_2$ $(r_1 > r_2)$ respectively are connected in series. This combination is connected to an external resistance '$R$'. It is observed that the potential difference across the cell $E_1$ becomes zero. The value of $R$ will be

The component of vector $\overrightarrow{A} = a_x \hat{i} + a_y \hat{j} + a_z \hat{k}$ along the direction of $\hat{i} - \hat{j}$ is

In the circuit shown in the figure,the $AC$ source gives a voltage $V = 20 \cos (2000 t)$. Neglecting source resistance,the voltmeter and ammeter readings will be: