A coil of inductive reactance 31 has a resistance of 8 . It is placed in series with a condenser of capacitative reactance 25 . The combination is connected to an a.c. source of 110 ~V . The power factor of the circuit

Correct answer: D. 0.80 X_L=31 , X_C=25 , R=8 impedance of series LCR is aligned & Z= R^2+(X_ L -X_ C )^2 & = 8^2+(31-25)^2 & = 64+36 = 100 =10 aligned Power factor φ= (R)/(2)=(8)/(10)= 0.8

NEET 2006

Exam: NEET
Year: 2006
Subject: Physics
Chapter: Alternating Current

NEET 2006 · Physics · Alternating Current

A coil of inductive reactance 31 has a resistance of 8 . It is...

A coil of inductive reactance

31 \Omega

has a resistance of

8 \Omega

. It is placed in series with a condenser of capacitative reactance

25 \Omega

. The combination is connected to an a.c. source of

110 \mathrm{~V}

. The power factor of the circuit is:

Options

A0.33
B0.56
C0.64
D0.80

Correct answer

D. 0.80

Step-by-step solution

X_L=31 \Omega, X_C=25 \Omega, R=8 \Omega\therefore

impedance of series LCR is

\begin{aligned}& \mathrm{Z}=\sqrt{\mathrm{R}^2+\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)^2}\\ & =\sqrt{8^2+(31-25)^2}\\ & =\sqrt{64+36}=\sqrt{100}=10 \Omega \end{aligned}

Power factor \cos \phi=

\frac{R}{2}=\frac{8}{10}=$0.8

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