Two cells having unknown emfs $E_1$ and $E_2$ $\left(E_1>E_2\right)$ are connected in potentiometer circuit, so as to assist each other. The null point obtained is at 490 cm from the higher potential end. When cell $E_2$ is connected, so as to oppose cell $E_1$, the null point is obtained at 90 cm from the same end. The ratio of the emfs of two cells $\left(\frac{E_1}{E_2}\right)$ is

A 10 m long wire of resistance $20 \Omega$ is connected in series with a battery of emf 3 V and a resistance of $10 \Omega$. The potential gradient along the wire in $\mathrm{V} / \mathrm{m}$ is

Two galvanometers $A$ and $B$ require currents of 4 mA and 7 mA , respectively to produce the same deflection of 20 divisions. If $S_A$ and $S_B$ are their sensitivities respectively, then

A circular coil of radius $$R$$ has a resistance of $$40 \Omega$$. Figure shows two points $$P$$ and $$Q$$ on the circumference separated by a distance $$\frac{\pi R}{2}$$ which are connected to a 16 V battery with internal resistance of $$0.5 \Omega$$. What is the value of current $$I$$ flowing through the circuit?