When the value of $R$ in the balanced Wheatstone bridge, shown in the figure, is increased from $5 \Omega$ to $7 \Omega$, the value of $S$ has to be increased by $3 \Omega$ in order to maintain the balance. What is the initial value of $S$ (in $\Omega$)?

To measure the temperature coefficient of resistivity $\alpha$ of a semiconductor,an electrical arrangement shown in the figure is prepared. The arm $BC$ is made up of the semiconductor. The experiment is being conducted at $25^{\circ} C$ and the resistance of the semiconductor arm $BC$ is $3 \ m\Omega$. Arm $BC$ is cooled at a constant rate of $2^{\circ} C / s$. If the galvanometer $G$ shows no deflection after $10 \ s$,then $\alpha$ is:

If the charge on the capacitor is $1 \text{ mC}$ in the given circuit,then $\frac{R_1 R_2}{R_3} = \ldots \ldots \ldots \Omega$.

For the circuit given below,the Kirchhoff's loop rule for the loop $BCDEB$ is given by the equation:

In the given circuit,current $I$ is independent of the resistance $R_6$. Then

$A$ uniform wire of $16\,\Omega$ is bent into the form of a square. Two opposite corners of the square are connected by a wire of resistance $16\,\Omega$. The effective resistance between the other two opposite corners is ............... $\Omega$.