The maximum power dissipated in an external resistance $R$,when connected to a cell of emf $\varepsilon$ and internal resistance $r$,will be . . . . . . .

In the given network,the current through branch $BG$ is almost equal to ............ $A$.

$A, B$ and $C$ are voltmeters of resistance $R, 1.5R$ and $3R$ respectively as shown in the figure. When some potential difference is applied between $X$ and $Y$,the voltmeter readings are $V_A, V_B$ and $V_C$ respectively. Then

Three resistors $1 \Omega, 2 \Omega$ and $3 \Omega$ are connected to form a triangle. Across the $3 \Omega$ resistor,a $3 \text{ V}$ battery is connected. The current through the $3 \Omega$ resistor is: (in $\text{ A}$)

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

In the circuit shown in the figure,switch $S_1$ is initially closed and $S_2$ is open. Find $V_a - V_b$ in $V$.