Two cells of internal resistance $r_{1}$ and $r_{2}$ and of the same emf are connected in series across a resistor of resistance $R$. If the terminal potential difference across the cell of internal resistance $r_{1}$ is zero,then the value of $R$ is

Explain the 'Mixed Connection' of cells and derive an expression for its equivalent emf and current.

When a resistor of $11 \,\Omega$ is connected in series with an electric cell,the current flowing in it is $0.5 \, A$. Instead,when a resistor of $5 \,\Omega$ is connected to the same electric cell in series,the current increases by $0.4 \, A$. The internal resistance of the cell is ................ $\Omega$.

When a current of $2\, A$ flows in a battery from negative to positive terminal, the potential difference across it is $12\, V$. If a current of $3\, A$ flowing in the opposite direction produces a potential difference of $15\, V$, the $emf$ of the battery is .............. $V$.

Two cells of emf $1 \ V$ and $2 \ V$ and internal resistance $2 \ \Omega$ and $1 \ \Omega$,respectively,are connected in series with an external resistance of $6 \ \Omega$. The total current in the circuit is $I_1$. Now the same two cells in parallel configuration are connected to the same external resistance. In this case,the total current drawn is $I_2$. The value of $\left(\frac{I_1}{I_2}\right)$ is $\frac{x}{3}$. The value of $x$ is . . . . . . .

$A$ cell of emf $1.2 \ V$ and internal resistance $2 \ \Omega$ is connected in parallel to another cell of emf $1.5 \ V$ and internal resistance $1 \ \Omega$. If the like poles of the cells are connected together,the emf of the combination of the two cells is (in $V$)