Two sources of equal emfs $E$ are connected in series. This combination is connected to an external resistance $R$. The internal resistances of the two sources are $r_{1}$ and $r_{2}$ $(r_{1} > r_{2})$. If the potential difference across the source of internal resistance $r_{1}$ is zero,then the value of $R$ will be:

Twelve cells,each having emf $E$ volts,are connected in series and are kept in a closed box. Some of these cells are wrongly connected with positive and negative terminals reversed. This $12$-cell battery is connected in series with an ammeter,an external resistance $R$ ohms,and a two-cell battery (two cells of the same type used earlier,connected perfectly in series). The current in the circuit when the $12$-cell battery and $2$-cell battery aid each other is $3 \text{ A}$,and it is $2 \text{ A}$ when they oppose each other. Then,the number of cells in the $12$-cell battery that are connected wrongly is:

Eels are able to generate current with biological cells called electroplaques. The electroplaques in an eel are arranged in $100$ rows,each row stretching horizontally along the body of the fish containing $5000$ electroplaques. The arrangement is shown below. Each electroplaque has an emf of $0.15\, V$ and internal resistance of $0.25\,\Omega$. The water surrounding the eel completes a circuit between the head and its tail. If the water surrounding it has a resistance of $500\,\Omega$,the current an eel can produce in water is about .............. $A$.

When a resistance of $2\,\Omega$ is connected across the terminals of a cell,the current is $0.5\,A$. When the resistance is increased to $5\,\Omega$,the current is $0.25\,A$. The internal resistance of the cell is ............. $\Omega$.

The internal resistance of a cell of emf $4 \text{ V}$ is $0.1 \ \Omega$. It is connected to an external resistance of $3.9 \ \Omega$. The terminal voltage across the cell will be . . . . . . . (in $\text{ V}$)

Four identical cells of $EMF$ $E$ and internal resistance $r$ are connected as shown in the figure. Find the terminal voltage across any one cell.