In the given figure,the equivalent resistance between the points $A$ and $B$ is ............ $\Omega$.

$A$ heater is designed to operate with a power of $1000 \ W$ in a $100 \ V$ line. It is connected in combination with a resistance of $10 \ \Omega$ and a resistance $R$,to a $100 \ V$ mains as shown in the figure. For the heater to operate at $62.5 \ W$,the value of $R$ should be .................. $\Omega$.

The resistance of a heater coil is $110\, \Omega$. $A$ resistance $R$ is connected in parallel with it,and the combination is joined in series with a resistance of $11\, \Omega$ to a $220\, V$ main line. The heater operates with a power of $110\, W$. The value of $R$ in $\Omega$ is

Find the current in the $6\,\Omega$ resistance.

In the circuit shown,the cells $A$ and $B$ have negligible internal resistances. For $V_A = 16 \ V$,$R_1 = 600 \ \Omega$,and $R = 200 \ \Omega$,the galvanometer shows no deflection. The value of $V_B$ is $...V$.

$A$ current of $1.5\, A$ flows through a copper voltameter. The thickness of copper deposited on the electrode surface of area $50\, cm^2$ in $20\, min$ will be (Density of copper $= 9000\, kg/m^3$ and $E.C.E.$ of copper $= 0.00033\, g/C$).