$A$ $50\,V$ battery is connected across a $10\,\Omega$ resistor. The current is $4.5\,A$. The internal resistance of the battery is ............. $\Omega$.

In the network shown in the figure,the potential difference across the $2R$ resistor is...... (The cell has an $emf$ $E$ and no internal resistance).

For a cell, the graph between the potential difference $(V)$ across the terminals of the cell and the current $(I)$ drawn from the cell is shown in the figure. The $e.m.f.$ and the internal resistance of the cell are

The figure shows a network of resistors and a battery. If $1\,A$ current flows through the branch $CF$,then answer the following questions. The current through:

$A$ heater is designed to operate with a power of $1000 \ W$ in a $100 \ V$ line. It is connected in combination with a resistance of $10 \ \Omega$ and a resistance $R$,to a $100 \ V$ mains as shown in the figure. For the heater to operate at $62.5 \ W$,the value of $R$ should be .................. $\Omega$.

$A$ wire of uniform resistance $\lambda \ \Omega/m$ is bent into a circle of radius $r$. Two radial wires, each of length $r$, are connected from the center $O$ to points $A$ and $B$ on the circumference, where the angle $\angle AOB = 90^\circ$. The equivalent resistance between points $A$ and $B$ is . . . . . . $\Omega$.