When cell of e.m.f. ' $E_1$ ' is connected to potentiometer wire, the balancing length is ' $l_l$ '. Another cell of e.m.f. ' $E_2$ ' $\left(E_1>E_2\right)$ is connected so that two cells oppose each other, the balancing length is ' $l_1$ '. The ratio $E_1: E_2$ is

In the given circuit, current flowing through the circuit is

The voltmeter has range 10 V and its internal resistance is $50 \Omega$. To increase the range of voltmeter to 15 V , the resistance which is to be connected is

In the given electrical network, the value of resistance ' $R$ ' when the current in the galvanometer will be zero, is