Alternating Current - Result Question 11

11. A series LCR circuit is connected to an ac voltage source. When L is removed from the circuit, the phase difference between current and voltage is π3. If instead C is removed from the circuit, the phase difference is again π3 between current and voltage. The power factor of the circuit is :

[2020]

(a) 0.5

(b) 1.0

(c) -1.0

(d) zero

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Answer:

Correct Answer: 11. (b)

Solution:

  1. (b) When L is removed,

Phase difference

(1)tanϕ=|XC|R=tanπ3=XCR

When C is removed,

Phase difference

(2)tanϕ=|XL|R=tanπ3=XLR

From eqs. (1) and (2), XL=XC

Since, XL=XC, the circuit is in resonance.

In this case, Z=R

Power factor, cosϕ=RZ=1.



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