A circuit with an electrical load having impedance $$Z$$ is connected with an AC source as shown in the diagram. The source voltage varies in time as $$V(t) = 300 \sin(400t)$$ V, where $$t$$ is time in s. List-I shows various options for the load. The possible currents $$i(t)$$ in the circuit as a function of time are given in List-II.

Choose the option that describes the correct match between the entries in List-I to those in List-II.

For P: $$\mathrm{i} = \frac{\mathrm{V}}{\mathrm{R}} = 10 \sin 400 \mathrm{t} \Rightarrow (3)$$

For Q: $$\mathrm{X}_{\mathrm{L}} = \omega \mathrm{L} = 400 \times 100 \times 10^{-3} = 40\ \Omega$$

$$\therefore \mathrm{Z} = 50\ \Omega$$

$$\therefore \mathrm{i} = \frac{300}{50} \sin \left(400 \mathrm{t} - 53^{\circ}\right)$$

[current will lag by $$\tan^{-1} \frac{\mathrm{X}_{\mathrm{L}}}{\mathrm{R}}$$] $$\Rightarrow (5)$$

For R: $$\mathrm{X}_{\mathrm{C}} = \frac{10^{6}}{400 \times 50}\ \Omega = 50\ \Omega\ \text{and}\ \mathrm{X}_{\mathrm{L}} = 400 \times 25 \times 10^{-3} = 10\ \Omega$$

$$\therefore \mathrm{Z} = 50\ \Omega$$

$$\therefore \mathrm{i} = \frac{300}{50} \sin \left(400 \mathrm{t} + 53^{\circ}\right)$$

Current will lead by $$\left[\tan^{-1} \frac{\mathrm{X}_{\mathrm{C}} - \mathrm{X}_{\mathrm{L}}}{\mathrm{R}}\right] \Rightarrow (2)$$

For S: $$\mathrm{X}_{\mathrm{C}} = 50\ \Omega\ \text{and}\ \mathrm{X}_{\mathrm{L}} = 400 \times 125 \times 10^{-3} = 50\ \Omega$$

$$\mathrm{R} = 60\ \Omega$$

$$\therefore \mathrm{i} = \frac{300}{60} \sin (400 \mathrm{t}) \quad \mathrm{X}_{\mathrm{L}} = \mathrm{X}_{\mathrm{C}} \Rightarrow \text{Resonance} \Rightarrow (1)$$