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Alternating Current question

2023 · 13 Apr · Shift 2 · Q57
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Alternating Current question

2023 · 13 Apr · Shift 2 · Q57

JEE MainPhysicsAlternating CurrentMCQ+4 / −1
Given below are two statements: Statement I : An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor. Statement II : An AC circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor. In the light of above statements, choose the correct answer form the options given below:
  1. A
    Both Statement I and Statement II are false
  2. B
    Statement I is true but statement II is false
  3. C
    Statement I is false but statement II is true
  4. D
    Both Statement I and Statement II are true
View written solutionFree

Correct answer: A

  1. Analyze Statement I

    Electrical resonance in an AC circuit occurs when the inductive reactance and capacitive reactance cancel each other: XL=XCX_L = X_CXL​=XC​ where XL=ωL,XC=1ωCX_L = \omega L, \qquad X_C = \frac{1}{\omega C}XL​=ωL,XC​=ωC1​

    So resonance requires both an inductor and a capacitor to be present in the circuit.

    A circuit containing only a capacitor or only an inductor cannot undergo resonance.

    Therefore, Statement I is false.

  2. Analyze Statement II

    For a pure capacitor or pure inductor, the phase difference between voltage and current is: ϕ=90∘\phi = 90^\circϕ=90∘

    Hence the power factor is: cos⁡ϕ=cos⁡90∘=0\cos\phi = \cos 90^\circ = 0cosϕ=cos90∘=0

    Average power consumed in an AC circuit is: P=VIcos⁡ϕP = VI\cos\phiP=VIcosϕ

    Thus, for a pure capacitor or pure inductor: P=VI⋅0=0P = VI \cdot 0 = 0P=VI⋅0=0

    So such a circuit does not consume high power; in fact, it consumes zero average power.

    Therefore, Statement II is false.

  3. Conclusion

    • Statement I: False
    • Statement II: False

    Hence the correct option is: A\boxed{\text{A}}A​

  4. Comparison with stored answer

    Stored correct answer: A

    My derived answer: A

    They match.

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