A series L, R circuit connected with an ac source has a power factor of . If the source of emf is changed to , the new power factor of the circuit will be

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
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 [2024]

1 $\frac{1}{\sqrt{2}}$

2 $\frac{1}{\sqrt{3}}$

3 $\frac{1}{\sqrt{5}}$

4 $\frac{1}{\sqrt{7}}$

Ans.
(3)

For first source power factor

$\cos ϕ = \frac{R}{Z} = \frac{R}{\sqrt{R^{2} + ω^{2} L^{2}}}$

$\Rightarrow \frac{1}{\sqrt{2}} = \frac{R}{\sqrt{R^{2} + ω^{2} L^{2}}} \Rightarrow R^{2} + ω^{2} L^{2} = 2 R^{2}$

$\Rightarrow R = ω L$

for second source, $ω^{'} = 2000 = 2 ω$

Power Factor = $\frac{R}{\sqrt{R^{2} + ω^{' 2} L^{2}}}$

$= \frac{ω L}{\sqrt{ω^{2} L^{2} + 4 ω^{2} L^{2}}} = \frac{ω L}{\sqrt{5 ω^{2} L^{2}}} = \frac{1}{\sqrt{5}}$

Want Us to Email you About Special Offers & Updates?