Two cells,having the same $e.m.f.$ $E$,are connected in series through an external resistance $R$. The cells have internal resistances $r_1$ and $r_2$ $(r_1 > r_2)$ respectively. When the circuit is closed,the potential difference across the first cell is zero. The value of $R$ is

$A$ cell of emf $10 \text{ V}$ and internal resistance $3 \Omega$ is connected in parallel with another cell of emf $7 \text{ V}$ and internal resistance $\frac{3}{5} \Omega$,such that their positive terminals are joined together and their negative terminals are joined together. Their combined positive terminal is joined with the negative terminal,and their combined negative terminal is joined with the positive terminal of a third cell of emf $20 \text{ V}$ with internal resistance $2 \Omega$. The combination can be replaced by a battery of emf $E$ and internal resistance $r$. The values of $E$ and $r$ are respectively:

In which of the following cells is the potential difference between the terminals of the cell greater than its $EMF$?

$12$ cells,each having the same emf $E$ and internal resistance $r$,are connected in series and kept in a closed box. Some of the cells are wrongly connected. This battery is connected in series with an ammeter and two cells,each identical to the previous cells. The current is $3 \, A$ when the external cells aid the battery and $2 \, A$ when the external cells oppose the battery. How many cells in the battery are wrongly connected?

Two identical cells send the same current in $2\,\Omega$ resistance,whether connected in series or in parallel. The internal resistance of the cell should be ............... $\Omega$.

$A$ galvanometer is connected in series with an unknown resistor $R$ and two identical batteries of $1.5\, V$ each. When the batteries are connected in series,the galvanometer shows a current of $1\, A$. When the batteries are connected in parallel,it shows a current of $0.6\, A$. The internal resistance of each battery is: