A series L,R circuit connected with an ac source E=(25 sin 1000 t) V has a power factor of frac 1 √(2) . If the source of emf is changed to E =(20 sin 2000 t) V , the new power factor of the circuit will be :

Physics · Alternating Current

JEE Main 2024 — 30 January, Shift 1 — Question 45

A series L,R circuit connected with an ac source $E=(25 \sin 1000 t) V$ has a power factor of $\frac{1}{\sqrt{2}}$ . If the source of emf is changed to $\mathrm{E}=(20 \sin 2000$ t) V , the new power factor of the circuit will be :

Option A:
$\frac{1}{\sqrt{2}}$
Option B:
$\frac{1}{\sqrt{3}}$
Option C:
$\frac{1}{\sqrt{5}}$
Correct
Option D:
$\frac{1}{\sqrt{7}}$

Answer: C

Step-by-step solution

$E=25 \sin (1000 t)$

$\cos \theta=\frac{1}{\sqrt{2}}$

LR circuit Initially

$\frac{R}{\omega_{1} L}=\frac{1}{\tan \theta}=\frac{1}{\tan 45^{\circ}}=1$

$X_{L}=\omega_{1} L$

$\omega_{2}=2 \omega_{1}$ , given

$\tan \theta^{\prime}=\frac{\omega_{2} L}{R}=\frac{2 \omega_{1} L}{R}$

$\tan \theta^{\prime}=2$

$\cos \theta^{\prime}=\frac{1}{\sqrt{5}}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 30 January, Shift 1
Subject: Physics
Chapter: Alternating Current
Topic: Series LCR Circuit and Power Factor

Primary coil of a transformer is connected to 220 V ac. Primary and secondary turns of the transforms are 100 and 10 respectively.…

Answer: C

Step-by-step solution

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