The given Wheatstone bridge is showing no deflection in the galvanometer joined between the points $B$ and $D$ (Figure). Calculate the value of $R$.

 

Three equal resistance each of $R$ $\mathrm{ohm}$ are connected as shown in the figure. A battery of $2 \mathrm{volts}$ of internal resistance $0.1 \mathrm{ohm}$ is connected across the circuit. Calculate the value of $R$ for which the heat generated in the external circuit is maximum.

In the circuit shown in the figure the heat produced in the $5 \mathrm{\Omega }$ resistor due to the current flowing through it is $10 \mathrm{calories} \mathrm{per} \mathrm{second}$.

The heat generated in the $4 \mathrm{\Omega }$ resistor is:

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

The equivalent resistance between the points $A$ and $B$ is:

A battery of internal resistance $4 \mathrm{ohm}$ is connected to the network of resistance as shown. In the order that the maximum power can be delivered to the network, the value of $R$ in $\mathrm{ohm}$ should be :

In these three circuits all the batteries are identical and have negligible internal resistance, and all the light bulbs are identical. Rank all $5$ light bulbs $(A\mathit{,}\mathit{ }B\mathit{,}\mathit{ }C\mathit{,}\mathit{ }D\mathit{,}\mathit{ }E)$ in order of brightness from brightest to dimmest.

Two nonideal batteries are connected in parallel. Consider the following statements.

$\left(\mathrm{I}\right)$ The equivalent emf is smaller than either of the two EMFs.

$\left(\mathrm{II}\right)$ The equivalent internal resistance is smaller than either of the two internal resistance.