SATHEE: Alternating Current - Result Question 26

Alternating Current - Result Question 26

26. 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 volt. The power factor of the circuit is [2006]

(a) 0.64

(b) 0.80

(d) 0.56

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Answer:

Correct Answer: 26. (b)

Solution:

(b) Power factor, $ϕ = \frac{R}{\sqrt{(ω L - \frac{1}{ω C})^{2} + R^{2}}}$

$= \frac{8}{\sqrt{(31 - 25)^{2} + 8^{2}}} = \frac{8}{\sqrt{6^{2} + 8^{2}}} = \frac{8}{10} = 0.8$

Power factor $= \cos θ = \frac{R}{Z}$

For purely inductive and purely capacitive circuits, $θ = 90^{\circ}$

Power factor $= \cos θ = \cos 90^{\circ} = θ$ For non-inductive circuit, $θ = 0^{\circ}$ $\cos θ = \cos 0^{\circ} = 1$

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Alternating Current - Result Question 26

26. A coil of inductive reactance 31Ω has a resistance of 8Ω. It is placed in series with a condenser of capacitative reactance 25Ω. The combination is connected to an a.c. source of 110 volt. The power factor of the circuit is [2006]

Answer:

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26. 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 volt. The power factor of the circuit is [2006]