Q39 / 54 · KVPY 2017 (5 Nov SA) · Physics
In the circuit shown below (on the left) the resistance and the emf source are both variable. The graph of seven readings of the voltmeter and the ammeter (V and I, respectively) for different setting of resistance and the emf, taken at equal intervals of time $\Delta t$, are shown (on the right) by the dots connected by the curve EFGH. Consider the interval resistance of the battery to be negligible and the voltmeter and ammeter to be ideal devices. Take $R_{0}=V_{0} I_{0}$
Then the plot of the resistance as a function of time corresponding to the curve EFGH is given by
Then the plot of the resistance as a function of time corresponding to the curve EFGH is given by
- A
- B
- C
- Correct answerD
Solution
From $\mathrm{E} \rightarrow \mathrm{F}$
Slope is constant
$V=\mid R$
Thus $R$ must be constant
$\mathrm{R}_{0}=\mathrm{V}_{0} / \mathrm{I}_{0}$
Frorm $\mathrm{F} \rightarrow \mathrm{G}$
$\mathrm{V}=$ constant
$\mathrm{I}$ is increase thus $\mathrm{R}$ must be decrease.
at $G, R=\frac{V_{0}}{2 I_{0}}=\frac{R_{0}}{2}$
From $\mathbf{G} \rightarrow \mathbf{H}$
$\mathrm{I}=$ constant
$\mathrm{V}=$ increase, thus $\mathrm{R}$ must be increase
$\mathrm{R}_{\mathrm{H}}=\frac{2 \mathrm{~V}_{0}}{2 \mathrm{l}_{0}}=\mathrm{R}_{0}$
Hence, the correct answer is option: 'D'.