Alternating Current Question 9
Question 9 - 2024 (30 Jan Shift 1)
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 $E=(20 \sin 2000 t) V$, the new power factor of the circuit will be:
(1) $\frac{1}{\sqrt{2}}$
(2) $\frac{1}{\sqrt{3}}$
(3) $\frac{1}{\sqrt{5}}$
(4) $\frac{1}{\sqrt{7}}$
Show Answer
Answer: (3)
Solution:
$E=25 \sin (1000 t)$
$\cos \theta=\frac{1}{\sqrt{2}}$
LR circuit
R
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
$\tan \theta^{\prime}=\frac{\omega _2 L}{R}=\frac{2 \omega _1 L}{R}$
$\tan \theta^{\prime}=2$
$\cos \theta^{\prime}=\frac{1}{\sqrt{5}}$
