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

Correct answer: (D) 0.80. X_L=31 Ω, X_C=25 Ω, R=8 Ω ∴ impedance of series LCR is Z=√R^2+ (X_L-X_C )^2 =√(8^2+(31-25)^2) =√(64+36)=√100=10 Ω Power factor cos φ=R/2=8/10=0.8

Q131 / 200 · NEET 2006 · Physics

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:

A
0.33
B
0.56
C
0.64
Correct answer
D
0.80

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

Hence, the correct answer is option: 'D'.

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:

Solution

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