Under what condition can the current passing through the resistance $R$ be increased by short-circuiting the battery of emf $E_2$? The internal resistances of the two batteries are $r_1$ and $r_2$ respectively.

If the resistance of the voltmeter is $10000 \,\Omega$ and the resistance of the ammeter is $2 \,\Omega$,find the value of $R$ when the voltmeter reads $12 \,V$ and the ammeter reads $0.1 \,A$.

In the figure,the value of the resistor to be connected between $C$ and $D$ so that the equivalent resistance of the entire circuit between $A$ and $B$ does not change with the number of elementary sets used is

The resistance of an iron wire is $10\,\Omega$ and the temperature coefficient of resistivity is $5 \times 10^{-3}\,^{\circ}C^{-1}$. At $20\,^{\circ}C$,it carries $30\,mA$ of current. Keeping the potential difference between its ends constant,the temperature of the wire is raised to $120\,^{\circ}C$. The current in milliamperes that flows in the wire is:

The potential difference $(V_A - V_B)$ between the points $A$ and $B$ in the given figure is ............ $V$.

In the circuit shown, the heat produced in $5 \Omega$ resistance due to current $I_2$ is $50 \text{ J/s}$. Then, the heat generated per second in $2 \Omega$ resistance is (in $\text{ J/s}$)