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Alternating Current question

2020 · Q160
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Alternating Current question

2020 · Q160

NEETPhysicsAlternating CurrentMCQ+4 / −1
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{\pi \over 3}3π​. If instead C is removed from the circuit, the phase difference is again π3{\pi \over 3}3π​ between current and voltage. The power factor of the circuit is :
  1. A
    0.5
  2. B
    1.0
  3. C
    −-− 1.0
  4. D
    zero
View written solutionFree

Correct answer: B

The power factor for the LCR circuit will be :
When L is removed,

tan⁡ϕ=∣XC∣R\tan \phi = {{\left| {{X_C}} \right|} \over R}tanϕ=R∣XC​∣​

⇒tan⁡π3=XCR \Rightarrow \tan {\pi \over 3} = {{{X_C}} \over R}⇒tan3π​=RXC​​ ...(i)

When C is removed,

tan⁡ϕ=∣XL∣R\tan \phi = {{\left| {{X_L}} \right|} \over R}tanϕ=R∣XL​∣​

⇒tan⁡π3=XLR \Rightarrow \tan {\pi \over 3} = {{{X_L}} \over R}⇒tan3π​=RXL​​ ...(ii)

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

Z = R

Power factor = cos ϕ\phi ϕ = RZ{R \over Z}ZR​ = 1

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