Two cells $E_1$ and $E_2$ having equal e.m.f ' $E$ ' and internal resistances $r_1$ and $r_2\left(r_1>r_2\right)$ 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

If the length of the oscillating simple pendulum is made $\frac{1}{3}$ times the original keeping amplitude same then increase in its total energy at a place will be

Two long conductors separated by a distance ' d ' carry currents ' $\mathrm{I}_1$ ' and ' $\mathrm{I}_2$ ' in the same directions. They exert a force ' $F$ ' on each other. The distance between them is increased to ' 3 d '. If new repulsive force of magnitude ' $\frac{2}{3} \mathrm{~F}$ ' is found between these conductors, the required change in the magnitude and direction of one of the currents in the conductor is respectively [length of the conductors is constant]

In a transistor amplifier, AC current gain is 64 , the load resistance is $5400 \Omega$ and the input resistance of the transistor is $540 \Omega$. The voltage gain is