When a resistance of $9 \,\Omega$ is connected across the terminals of a battery,its potential difference decreases from $40 \, V$ to $30 \, V$. The internal resistance of the battery is ............... $\Omega$.

$A$ resistance network is connected to a battery as shown in the figure below. If the internal resistance of the battery is $5 \ \Omega$,then the value of $R$ (in $\Omega$) for maximum power delivered to the network is

$A$ wire of cross-section area $A$,length $L_1$,resistivity $\rho_1$ and temperature coefficient of resistivity $\alpha_1$ is connected to a second wire of length $L_2$,resistivity $\rho_2$,temperature coefficient of resistivity $\alpha_2$ and the same area $A$,so that the wires carry the same current. The total resistance $R$ is independent of temperature for small temperature changes if (Thermal expansion effect is negligible):

Inside a superconducting ring,six identical resistors each of resistance $R$ are connected as shown in the figure. Imagine a battery of $emf$ $E$ connected between points $O$ and $1$,with its positive terminal connected to $O$.

In the given circuit,$(V_A - V_B) = \dots \dots \dots V$.

Three equal resistors connected in series across a source of $e.m.f.$ together dissipate $10 \ W$. If the same resistors are connected in parallel across the same $e.m.f.$,then the power dissipated will be .............. $W$.