Five equal resistances are connected in a network as shown in figure. The net resistance between the points $A$ and $B$ is :

A potentiometer wire $PQ$ of $1 \mathrm{m}$ length is connected to a standard cell $E_1$. Another cell $E_2$ of emf $1.02 \mathrm{V}$ is connected with a resistance $r$ and switch $S$ (as shown in figure). With switch $S$ open, the null position is obtained at a distance of $49 \mathrm{cm}$ from $\mathrm{Q}$. The potential gradient in the potentiometer wire is :

An ideal cell of emf $10 \mathrm{V}$ is connected in circuit shown in figure. Each resistance is $2 \mathrm{\Omega }$. The potential difference (in $\mathrm{V}$) across the capacitor when it is fully charged is _____________

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 :