Find the current in the loop.

$A$ simple circuit contains an ideal battery and a resistance $R$. If a second resistor is placed in parallel with the first,which of the following statements is correct?

Two long coaxial and conducting cylinders of radius $a$ and $b$ are separated by a material of conductivity $\sigma$ and a constant potential difference $V$ is maintained between them by a battery. Then the current per unit length of the cylinder flowing from one cylinder to the other is -

$A$ battery of internal resistance $4 \,\Omega$ is connected to the network of resistances as shown. In order to give the maximum power to the network,the value of $R$ (in $\Omega$) should be

The potential drop across the $3 \,\Omega$ resistor is ............... $V$.

Two electric bulbs whose resistances are in the ratio of $1 : 2$ are connected in parallel to a constant voltage source. The powers dissipated in them have the ratio: