$A$ current of $2.0 \, A$ passes through a cell of $e.m.f.$ $1.5 \, V$ having an internal resistance of $0.15 \, \Omega$. The potential difference measured,in $volts$,across the terminals of the cell will be:

If the galvanometer $G$ does not show any deflection in the circuit shown,the value of $R$ is given by $............\Omega$.

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

In the circuit given below,if the bulb is to glow with maximum intensity,the value of $R$ is (neglect internal resistance of the cell) (in $\Omega$)

One end each of a resistance $r$,a capacitor $C$,and a resistance $2r$ are connected together. The other ends are respectively connected to the positive terminals of batteries $P$,$Q$,and $R$ having emfs $E$,$E$,and $2E$. The negative terminals of the batteries are then connected together. In this circuit,with steady current,the potential drop across the capacitor 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: