$A$ cell of $e.m.f.$ $1.5\,V$ having a finite internal resistance is connected to a load resistance of $2\,\Omega$. For maximum power transfer,the internal resistance of the cell should be ............. $\Omega$.

As shown in the figure,a network of resistors is connected to a battery of $24\,V$ with an internal resistance of $3\,\Omega$. The currents through the resistors $R_4$ and $R_5$ are $I_4$ and $I_5$ respectively. The values of $I_4$ and $I_5$ are:

The resistance of a heater coil is $110\, \Omega$. $A$ resistance $R$ is connected in parallel with it,and the combination is joined in series with a resistance of $11\, \Omega$ to a $220\, V$ main line. The heater operates with a power of $110\, W$. The value of $R$ in $\Omega$ is

In the figure shown, if the internal resistance of the battery is $1\, \Omega$, the reading of the ammeter will be ................. $A$.

The resistances in the following circuit are $R_1 = R_2 = R_3 = 6.0 \ \Omega$. The emf of the battery is $12 \ V$. When switch $S$ is closed, the potential across resistance $R_1$ changes by an amount:

$A$ constant voltage is applied between the two ends of a uniform metallic wire. Some heat is developed in it. The heat developed is doubled if