Question

An ammeter and a voltmeter of resistance R are connected in series to a electric cell of negligible internal resistance. Their reading are A
and V respectively. If another resistance R is connected in parallel with the voltmeter, then
(a) both A and V will increase
(b) both A and V will decrease
(c) A will decrease and V will increase
(d) A will increase and V will decrease

Answer 1

$$\begin{gathered} \mathrm{Case}\mathrm{I}:(\mathrm{without}\mathrm{external}\mathrm{resistance}\mathrm{R}) \\ \mathrm{Let} \\ \mathrm{Resistance}\mathrm{of}\mathrm{ammeter}=\mathrm{R} \\ \mathrm{Resistance}\mathrm{of}\mathrm{voltmeter}=\mathrm{R} \\ \mathrm{Ammeter}\mathrm{reading}: \\ \mathrm{A}=\frac{\mathrm{Total}\mathrm{emf}}{\mathrm{Total}\mathrm{resistance}} \\ =\frac{\mathrm{E}}{\mathrm{R}+\mathrm{R}} \\ =\frac{\mathrm{E}}{2\mathrm{R}} \\ =\frac{0.5\mathrm{E}}{\mathrm{R}} \\ \mathrm{Voltmeter}\mathrm{reading}: \\ \mathrm{V}=\mathrm{IR} \\ =\mathrm{AR} \\ =\frac{\mathrm{E}}{2\mathrm{R}}\times \mathrm{R} \\ =\frac{\mathrm{E}}{2} \\ \mathrm{Case}\mathrm{II}:(\mathrm{with}\mathrm{external}\mathrm{resistance}\mathrm{R}) \\ \mathrm{New}\mathrm{resistance}\mathrm{of}\mathrm{voltmeter}: \\ \mathrm{R}\text{'}=\mathrm{R}\mathrm{and}\mathrm{R}\mathrm{in}\mathrm{parallel} \\ =\frac{\mathrm{R}\times \mathrm{R}}{\mathrm{R}+\mathrm{R}} \\ =\frac{\mathrm{R}}{2} \\ \mathbf{Ammeter}\mathbf{}\mathbf{reading}\mathbf{:} \\ \mathrm{A}\text{'}=\frac{\mathrm{Total}\mathrm{emf}}{\mathrm{Total}\mathrm{resistance}} \\ =\frac{\mathrm{E}}{\mathrm{R}+{\displaystyle \frac{\mathrm{R}}{2}}} \\ =\frac{2\mathrm{E}}{3\mathrm{R}} \\ =\frac{0.67\mathrm{E}}{\mathrm{R}} \\ >\mathrm{A} \\ \mathbf{Voltmeter}\mathbf{}\mathbf{reading}\mathbf{:} \\ \mathrm{V}\text{'}=\mathrm{IR} \\ =\mathrm{A}\text{'}\mathrm{R} \\ =\frac{2\mathrm{E}}{3\mathrm{R}}\times \frac{\mathrm{R}}{2} \\ =0.33\mathrm{E} \\ <\mathrm{V} \\ \mathbf{Answer}\mathbf{:} \\ \mathrm{Ammeter}\mathrm{reading}\mathrm{decreases}\mathrm{and}\mathrm{voltmeter}\mathrm{reading}\mathrm{increases} \end{gathered}$$