In the circuit shown in the figure,switch $S_1$ is initially closed and $S_2$ is open. Find $V_a - V_b$ in $V$.

Six equal resistances $R$ are connected between points $P$,$Q$,and $R$ as shown in the figure. Then the net resistance will be maximum between:

$A$ uniform wire of resistance $9 \, \Omega$ is cut into $3$ equal parts. They are connected in the form of an equilateral triangle $ABC$. $A$ cell of $e.m.f.$ $2 \, V$ and negligible internal resistance is connected across $B$ and $C$. The potential difference across $AB$ is ............... $V$.

An infinite sequence of resistors is shown in the figure. The resultant resistance between $A$ and $B$ will be,when $R_1 = 1\,\Omega$ and $R_2 = 2\,\Omega$ ............. $\Omega$

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 $\%$)

Two equal resistances, $400 \Omega$ each, are connected in series with an $8 V$ battery. If the resistance of the first one increases by $0.5 \%$, what is the change required in the resistance of the second one in order to keep the potential difference across it unaltered?