$A$ $50\, W$ bulb is in series with a room heater and the combination is connected across the mains. To get maximum heater output,the $50\, W$ bulb should be replaced by a bulb of: (in $, W$)

Calculate the voltage across $AB$ terminals in the given circuit.

In the given circuit,the internal resistance of the cell is zero. If $i_1$ and $i_2$ are the readings of the ammeter when the key $(K)$ is opened and closed respectively,then $i_1: i_2=$

For the given circuit,$V_A - V_C = \text{ . . . . . . } \ V$.

An ammeter and a voltmeter of resistance $R$ are connected in series to an electric cell of negligible internal resistance. Their readings are $A$ and $V$ respectively. If another resistance $R$ is connected in parallel with the voltmeter, what happens to the readings $A$ and $V$?

An infinite ladder network of resistors is shown in the figure. If $R_1 = 1 \, \Omega$ and $R_2 = 2 \, \Omega$,then the equivalent resistance between $A$ and $B$ is ................ $\Omega$.