Physics · Alternating Current

JEE Advanced 2025 — Paper 1 — Question 13

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 $V(t)=300 \sin (400 t) \mathrm{V}$ , 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

Option A:
$\mathrm{P} \rightarrow 3, \mathrm{Q} \rightarrow 5, \mathrm{R} \rightarrow 2, \mathrm{~S} \rightarrow 1$
Correct
Option B:
$\mathrm{P} \rightarrow 1, \mathrm{Q} \rightarrow 5, \mathrm{R} \rightarrow 2, \mathrm{~S} \rightarrow 3$
Option C:
$\mathrm{P} \rightarrow 3, \mathrm{Q} \rightarrow 4, \mathrm{R} \rightarrow 2, \mathrm{~S} \rightarrow 1$
Option D:
$\mathrm{P} \rightarrow 1, \mathrm{Q} \rightarrow 4, \mathrm{R} \rightarrow 2, \mathrm{~S} \rightarrow 5$

Answer: A

Step-by-step solution

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 $\mathrm{X}_{\mathrm{C}}=\frac{10^{6}}{400 \times 50} \Omega=50 \Omega$ and $\mathrm{X}_{\mathrm{L}}=400 \times 25 \times 10^{-3}=10 \Omega$ $\therefore \mathrm{Z}=50 \Omega$

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

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

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

$\mathrm{R}=60 \Omega$

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

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2025
Paper: Paper 1
Subject: Physics
Chapter: Alternating Current
Topic: Series LCR Circuit and Power Factor