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Current Electricity

Question
CBSEENPH12039845

In an electrical circuit R, L, C and AC voltage source are all connected in series when L is removed from the circuit, the phase difference between the voltage and the current in the circuit is π/3. If instead, Cis removed from the circuit, the phase difference is again π/3. The power factor of the circuit is

  • 1/2

  • 1 divided by square root of 2
  • 1

  • square root of 3 divided by 2

Solution

C.

1

Here, phase difference
tan space straight ϕ space equals space fraction numerator straight X subscript straight L minus straight X subscript straight C over denominator straight R end fraction
tan straight pi over 3 space equals space fraction numerator straight X subscript straight L minus straight X subscript straight C over denominator straight R end fraction
When space straight L space is space removed
square root of 3 space equals space straight X subscript straight C over straight R
straight X subscript straight C space equals space square root of 3 straight R end root
When space straight C space is space removed
tan straight pi over 3 space equals space square root of 3 space equals space straight X subscript straight L over straight R
straight X subscript straight L space equals straight R square root of 3
Hence comma space in space resonant space circuit
tan space straight ϕ space equals space fraction numerator square root of 3 straight R end root minus square root of 3 straight R end root over denominator straight R end fraction space equals 0
straight ϕ space equals 0
therefore space Power space factor space cos space straight ϕ space equals space 1
It is a condition of resonance, therefore, phase difference between voltage and current is zero and power factor is cos Φ = 1.

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