The emf of a cell of internal resistance $2 \ \Omega$ is measured using a voltmeter of resistance $998 \ \Omega$. The error in the emf measured is (in $\%$)

Consider the circuit shown in the figure. The value of the resistance $X$ for which the thermal power generated in it is independent of small variations of its resistance is

In the circuit shown,what is the value of the unknown resistance $R$ such that the total resistance between points $P$ and $Q$ is also equal to $R$?

Each of the resistances in the network shown in the figure is equal to $R$. The resistance between the terminals $A$ and $B$ is

$A$ $d.c.$ main supply of $e.m.f. \, 220 \, V$ is connected across a storage battery of $e.m.f. \, 200 \, V$ through a resistance of $1 \, \Omega$. The battery terminals are connected to an external resistance $'R'$. The minimum value of $'R'$ so that a current passes through the battery to charge it is ............... $\Omega$.

Find the current flowing through the resistance $R_2$ of the circuit shown in the figure,if the resistances are $R_1 = 20 \ \Omega, R_2 = 30 \ \Omega$ and $R_3 = 60 \ \Omega$,and the potentials of points $1, 2$ and $3$ are $V_1 = 20 \ V, V_2 = 30 \ V$ and $V_3 = 60 \ V$ respectively. (in $A$)