In the circuits shown below, the readings of the voltmeters and the ammeters will be:

Find the $emf$ $(E)$ of the cell in $V$ required to light the bulb rated $4.5 \, W, 1.5 \, V$ fully,as shown in the circuit.

The ammeter $A$ reads $2\, A$ and the voltmeter $V$ reads $20\, V$. The value of resistance $R$ is (Assuming finite resistances of ammeter and voltmeter).

The maximum power dissipated in an external resistance $R$,when connected to a cell of emf $\varepsilon$ and internal resistance $r$,will be . . . . . . .

Two bulbs,as in the previous context ($40\, W$ and $100\, W$ bulbs rated at the same voltage),are connected in series to a $200\, V$ line. Then:

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 $\delta R_P \approx \delta R_Q$?