$A$ copper voltameter is connected to a $12 \, V$ source,and $2 \, g$ of copper is deposited in $30 \, min$. If this cell is connected to a $6 \, V$ source,how much copper (in $g$) will be deposited in $45 \, min$?

Consider the two circuits $P$ and $Q$ shown below,which are used to measure the unknown resistance $R$. In each case,the resistance is estimated by using Ohm's law $R_{\text{est}} = \frac{V}{I}$,where $V$ and $I$ are the readings of the voltmeter and the ammeter,respectively. The meter resistances $R_V$ and $R_A$ are such that $R_A \ll R \ll R_V$. The internal resistance of the battery may be ignored. The absolute error in the estimate of the resistance is denoted by $\delta R = |R - R_{\text{est}}|$.
$(a)$ Express $\delta R_P$ in terms of the given resistance values.
$(b)$ Express $\delta R_Q$ in terms of the given resistance values.
$(c)$ For what value of $R$ will $\delta R_P \approx \delta R_Q$?

In the circuit shown,the point '$B$' is earthed. The potential at the point '$A$' is ............. $V$.

$A$ cell of $e.m.f.$ $1.5\,V$ having a finite internal resistance is connected to a load resistance of $2\,\Omega$. For maximum power transfer,the internal resistance of the cell should be ............. $\Omega$.

Consider an infinite ladder network shown in the figure. $V$ voltage $V$ is applied between the points $A$ and $B$. This applied voltage is halved after each section.

An ammeter and a voltmeter of resistance $R$ are connected in series to an electric cell of negligible internal resistance. Their readings are $A$ and $V$ respectively. If another resistance $R$ is connected in parallel with the voltmeter, what happens to the readings $A$ and $V$?