Question

In $AC$ circuit with source voltage $E$ = $20$ $sin\; 1000 \;t$ is connected to series $L-R$ circuit whose power factor is $\frac{1}{\sqrt 2}$ If $E = 25$ $sin \;2000$ $t$, the new power factor is :

• A. $\frac{2}{\sqrt5}$
• B. $\frac{1}{\sqrt5}$
• C. $\frac{1}{\sqrt3}$
• D. $\sqrt{(\frac{3}{5}})$

Answer 1

Answer: (B)

$\frac{1}{\sqrt5}$

Answer 2

The Correct Option is (B) : $\frac{1}{\sqrt5}$
Old :

New :
R = 1000 L

$\cos\theta=\frac{R}{Z}$
$=\frac{1000L}{\sqrt{(1000L)^2+(2000L)^2}}$
$=\frac{1}{\sqrt{1+4}}$
$=\frac{1}{\sqrt5}$