$A$ cell of constant $e.m.f.$ is first connected to a resistance $R_1$ and then connected to a resistance $R_2$. If the power delivered in both cases is the same,then the internal resistance of the cell is:

The potential difference $(V_A - V_B)$ between the points $A$ and $B$ in the given figure is ............ $V$.

What is the current $i$ in the circuit as shown in the figure (in $A$)?

Two resistors are connected in series across a battery as shown in the figure. If a voltmeter of resistance $2000 \,\Omega$ is used to measure the potential difference across the $500 \,\Omega$ resistor,the reading of the voltmeter will be ............... $V$.

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 $\delta R_P \approx \delta R_Q$?

For the circuits $A$ and $B$ as shown in the figure,identify the correct option.