In the circuit shown in the figure, if the power consumed by the 5 Ω resistor is 10 W, then the power factor of the circuit is

F1 Raviranjan 13-1-22 Savita D1

This question was previously asked in
UKPSC JE Electrical 2013 Official Paper II (Held on 7 Nov 2015)
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  1. 0.8
  2. 0.5
  3. 0.6
  4. 0

Answer (Detailed Solution Below)

Option 3 : 0.6
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Concept:

F1 Raviranjan 13-1-22 Savita D1

The given circuit is R-L series circuit. Therefore current will be equal in all the element.

Given, Power consumed by 5 Ω resister is 10 W.

i.e, \(\rm I^2_{rms}=10\)

⇒ \(\rm I^2_{rms}=\frac{10}{5}=2\ A\)

⇒ Irms = √2 A

Vs = 50 sin ωt

Vsrms = 50 / √2 

∴ \(\rm z=\frac{V_{srms}}{I_{rms}}=\frac{50/√{2}}{√{2}} Ω=25\ Ω\)

req = 5 + 10 = 15 Ω

∴ \(\rm \cos\phi=\frac{R_{eq}}{z_{eq}}=\frac{15}{25}=0.6\)

Therefore, correct option will be 3.

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