Find the current through $25 \mathrm{V}$ cell (in $A$ ) in the figure shown.

 

Find the product of emf $\left(V\right)$ and internal resistance $\left(r\right)$ of a single battery which is equivalent to a parallel combination of two batteries of emfs $V_1$ and $V_2$ and internal resistance $r_1$ and $r_2$ respectively, with polarities as shown in figure. [Given : $V_1=15 V,{ V}_2=5 V,r_1=1\Omega ,r_2=1\Omega$]

For what value of $R$ in circuit, current through $4\Omega$ resistance is zero?

At what value of the resistance $R_x$ in the circuit shown in figure will the total resistance between points $A$and $B$ be independent of the number of loops? [Given : $R=(\sqrt{3}+1)$]

All batteries are having emf $10$ volt and internal resistance negligible. All resistors are in ohms. Calculate, the current in the right most $2\Omega$ resistor.

Find current in the branch $CD$ of the circuit (in ampere).

Relation between current in conductor and time is shown in figure. If resistance of conductor is $R=3\Omega$ then find total heat dissipated (in $J$) across resistance $R$.