Two cells of internal resistances $r_1$ and $r_2$ and of same emf are connected in series, across a resistor of resistance $R$. If the terminal potential difference across the cells of internal resistance $r_1$ is zero, then the value of $R$ is

The $I-V$ graphs for two different electrical appliances $P$ and $Q$ are shown in the diagram: If $R_P$ and $R_Q$ be the resistances of the devices, then

A galvanometer of resistance $50 \Omega$ is connected to a battery of $3 \cdot \mathrm{~V}$ along with a${ }^{\text { }}$ resistance of $2950 \Omega$ in series shows full-scale deflection of 30 divisions. The additional series resistance required to reduce the deflection to 20 divisions is