An alternating voltage e =200 sin 100 t is applied to a series combination of R =30 Ω and an inductor of 400 mH. The power factor of the circuit is:

Question

An alternating voltage e =200 sin 100 t is applied to a series combination of R =30 Ω and an inductor of 400 mH. The power factor of the circuit is: (A) 0.01 (B) 0.2 (C) 0.05 (D) 0.6

Tardigrade Admin · Accepted Answer

Power factor cos φ=( R / Z ) Z=√R2+XL2=√R2+(ω L)2 Z=√(30)2+(100 × 400 × 10-3)2=√900+1600=√2500 Z=50 Ω ∴ cos φ=(R/Z)=(30/50)=0.6

Q. An alternating voltage $e = 200 sin 100 t$ is applied to a series combination of $R = 30Ω$ and an inductor of 400 $m H$ . The power factor of the circuit is:

0.01

0.2

0.05

0.6

Power factor $cos ϕ = \frac{R}{Z}$
$Z = R^{2} + X_{L}^{2} = R^{2} + (ω L)^{2}$
$Z = (30)^{2} + (100 \times 400 \times 1 0^{- 3})^{2} = 900 + 1600 = 2500$
$Z = 50Ω$
$∴ cos ϕ = \frac{R}{Z} = \frac{30}{50} = 0.6$

Q. An alternating voltage e=200sin100t is applied to a series combination of R=30Ω and an inductor of 400 mH. The power factor of the circuit is:

0.01

0.2

0.05

0.6

Power factor cosϕ=ZR​ Z=R2+XL2​​=R2+(ωL)2​ Z=(30)2+(100×400×10−3)2​=900+1600​=2500​ Z=50Ω ∴cosϕ=ZR​=5030​=0.6

Q. An alternating voltage $e = 200 sin 100 t$ is applied to a series combination of $R = 30Ω$ and an inductor of 400 $m H$ . The power factor of the circuit is:

Power factor $cos ϕ = \frac{R}{Z}$
$Z = R^{2} + X_{L}^{2} = R^{2} + (ω L)^{2}$
$Z = (30)^{2} + (100 \times 400 \times 1 0^{- 3})^{2} = 900 + 1600 = 2500$
$Z = 50Ω$
$∴ cos ϕ = \frac{R}{Z} = \frac{30}{50} = 0.6$