In the given circuit,the galvanometer reading is zero. If the internal resistance of the cells is negligible,then the value of $x$ is ............. $\Omega$.

The circuit shown is in a steady state. Now,when the switch is closed,the galvanometer shows no deflection. Then the correct relation is:

The Wheatstone bridge principle is used to measure the specific resistance $(S_1)$ of a given wire,having length $L$ and radius $r$. If $X$ is the resistance of the wire,then the specific resistance is: $S_1 = X \left( \frac{\pi r^2}{L} \right)$. If the length of the wire is doubled,then the value of the specific resistance will be:

Determine the current in each branch of the network shown in the Figure.

Seven resistances are connected as shown in the figure. The equivalent resistance between $A$ and $B$ is ............... $\Omega$.

$A$ $6 \, V$ cell with $0.5 \, \Omega$ internal resistance, a $10 \, V$ cell with $1 \, \Omega$ internal resistance, and a $12 \, \Omega$ external resistance are connected in parallel. The current (in ampere) through the $10 \, V$ cell is