An infinite ladder network is arranged with resistances $R$ and $2R$ as shown. The effective resistance between terminals $A$ and $B$ is

For the given circuit,the $emf$ of the cells are $E_1 = 4 \, V$ and $E_2 = 8 \, V$,and their internal resistances are $0.5 \, \Omega$ and $1 \, \Omega$ respectively. Calculate the terminal voltage of each cell.

$A$ battery has an $e.m.f.$ of $4 \ V$ and an internal resistance of $r$. When the battery is connected to an external resistance of $2 \ \Omega$,a current of $1 \ A$ flows through the circuit. If the terminals of the battery are short-circuited (connected directly),what will be the current in $A$ flowing through it?

Find the current in the $10 \, \Omega$ resistance.

$A$ cell of $emf$ $E$ and internal resistance $r$ is connected in series with an external resistance $nr$. Then,the ratio of the terminal potential difference to $emf$ is

$A$ wire of resistance $R$ is bent in the form of a circular loop. Two points on the circle separated by a quarter circumference are connected to a battery of emf $E$ and negligible internal resistance. The heat generated in the wire per second is