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 $\mathrm{E}=(20 \sin 2000 \mathrm{t}) \mathrm{V}$, 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:
$\mathrm{E}=25 \sin (1000 \mathrm{t})$
$\cos \theta=\frac{1}{\sqrt{2}}$
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
$\tan \theta^{\prime}=\frac{\omega_{2} L}{R}=\frac{2 \omega_{1} L}{R}$
$\tan \theta^{\prime}=2$
$\cos \theta^{\prime}=\frac{1}{\sqrt{5}}$
