Cells in Series and in Parallel

Two cells, each of emf $1.5 \mathrm{V}$ are joined in series and send $1.0 \mathrm{A}$ current in an external resistor. If the same cells are joined in parallel, then they send $0.6 \mathrm{A}$ current in the same resistor. What is the internal resistance of each cell?

Prove that two identical cells (each of emf $E$, internal resistance $r$) will send same current in an external resistance $R$ whether all cells are connected in series or in parallel, if $R=r$.

Find the emf and the internal resistance of an electric source which is equivalent to two batteries of emf's $E_1$ and $E_2$ and internal resistances $r_1$ and $r_2$ connected in parallel.

Find the emf of the battery shown in figure.

$\mathrm{n}$ identical cells, each of emf E and internal resistance $\mathrm{r}$, are connected in series to a resistor $\mathrm{R}$. Deduce an expression for the internal resistance $\mathrm{r}$ of one cell in terms of the current $\mathrm{I}$ in the circuit.

In the Fig., what is the potential difference $V_d-V_c$ between the points $d$ and $c$ if ${\mathcal{E}}_1=4.0 \mathrm{V}, {\mathcal{E}}_2=1.0 \mathrm{V}, R_1=R_2=10 \mathrm{\Omega },$ and$R_3=8.0 \mathrm{\Omega }$ and the battery is ideal?

In figure, battery $1$ has ${\epsilon }_1=12.0 \mathrm{V}$ and internal resistance $r_1=0.025 \mathrm{\Omega }$ and battery $2$ has emf ${\epsilon }_2=12.0 \mathrm{V}$ and internal resistance $r_2=0.012 \mathrm{\Omega }$. The batteries are connected in series with an external resistance $R$. (a) What $R$ value makes the terminal-to-terminal potential difference of one of the batteries zero? (b) Which battery is that?

Find the emf and the internal resistance of a source which is equivalent to two batteries connected in parallel whose emf's are equal to ${\mathcal{E}}_1$ and ${\mathcal{E}}_2$ and internal resistances to $R_1$ and $R_2$.

There are two cells of emf ${\epsilon }_1$ and ${\epsilon }_2$ and internal resistance $r_1$ and $r_2$ respectively connected in parallel. Then find out the equivalent emf and equivalent internal resistance of this combination. If external resistance $R$ is connected to this combination, then find out the value of electric current flowing through $R$.

Six lead-acid type of secondary cells each of emf $2.0 \mathrm{V}$ and internal resistance $0.015 \mathrm{\Omega }$ are joined in series to provide a supply to the resistance of $8.5 \mathrm{\Omega }$. What is the current drawn from the supply and its terminal voltage?