The current flowing in the given circuit is $0.1\,A$. The potential difference between the points $X$ and $Y$ is ................ $V$.

$A$ current of $6\, A$ enters at corner $P$ of an equilateral triangle $PQR$ having $3$ wires of resistance $2 \,\Omega$ each and leaves by the corner $R$. The current $i_{1}$ in ampere is ........ .

The potential difference across $A$ and $B$,i.e.,$V_A - V_B$,is ......... $V$.

Model a torch battery of length $l$ to be made up of a thin cylindrical bar of radius $a$ and a concentric thin cylindrical shell of radius $b$,filled in between with an electrolyte of resistivity $\rho$ (see figure). If the battery is connected to a resistance of value $R$,the maximum Joule heating in $R$ will take place for:

In the circuit shown,the reading of the ammeter (ideal) is the same with both switches open as with both closed. Find the value of resistance $R$ in $\Omega$.

When a potential difference $V$ is applied across a wire of resistance $R$,it dissipates energy at a rate $W$. If the wire is cut into two halves and these halves are connected in parallel across the same supply,the energy dissipation rate will become: