$A$ circuit containing five resistors is connected to a battery with a $12 \,V$ emf as shown in the figure. The potential difference across the $4 \,\Omega$ resistor is ........... $V$.

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

An electric bulb rated for $500\, W$ at $100\, V$ is used in a circuit having a $200\, V$ supply. The resistance $R$ that must be put in series with the bulb,so that the bulb draws $500\, W$,is ................. $\Omega$.

One end each of a resistance $r$,a capacitor $C$,and a resistance $2r$ are connected together. The other ends are respectively connected to the positive terminals of batteries $P$,$Q$,and $R$ having emfs $E$,$E$,and $2E$. The negative terminals of the batteries are then connected together. In this circuit,with steady current,the potential drop across the capacitor is:

If each resistance in the figure is of $9\,\Omega$,then the reading of the ammeter is ............ $A$.

$A$ 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 . . . . . . $\Omega$.