Derive the potential difference across the terminals of a cell when circuit is open.

A battery of e.m.f $12 \mathrm{V}$ and internal resistance $0.5 \mathrm{\Omega }$ is charged by a battery charger which supplies a $132 \mathrm{V}$ d.c. supply using a series resistance of $11.5 \mathrm{\Omega }$. What is the terminal voltage of the battery during charging?

In the network shown, the equivalent resistance between $\mathrm{A}$ and $\mathrm{B}$ is $\frac{4}{3}\mathrm{\Omega }$, find the value of $\mathrm{r}$.

Consider an electrical conductor connected across a potential difference $V.$ Let $\Delta q$ be a small charge moving through it in time $\Delta t$. If $I$ is the electric current through it,
(i) the kinetic energy of the charge increases by $IV\Delta t$
(ii) the electric potential energy of the charge decreases by $IV\Delta \mathrm{t}$.
(iii) the thermal energy of the conductor increases by $IV\Delta \mathrm{t}$.

Then the correct statements is/are

Two cells of the same EMF $E$ but different internal resistances $r_1$ and $r_2$ are connected in series with an external resistance $R$ as shown in the figure. The terminal potential difference across, the second cell is found to be zero. The external resistance $R$ must then be: