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Alternating Current question

2021 · 31 Aug · Shift 1 · Q61
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Alternating Current question

2021 · 31 Aug · Shift 1 · Q61

JEE MainPhysicsAlternating CurrentMCQ+4 / −1
In an ac circuit, an inductor, a capacitor and a resistor are connected in series with XL = R = XC. Impedance of this circuit is :
  1. A
    2R2
  2. B
    Zero
  3. C
    R
  4. D
    R 2\sqrt 22​
View written solutionFree

Correct answer: C

  1. For a series RLCRLCRLC circuit, the impedance is
Z=R2+(XL−XC)2Z = \sqrt{R^2 + (X_L - X_C)^2}Z=R2+(XL​−XC​)2​

where:

  • RRR is resistance
  • XLX_LXL​ is inductive reactance
  • XCX_CXC​ is capacitive reactance
  1. Given in the question:
XL=R=XCX_L = R = X_CXL​=R=XC​

So,

XL−XC=0X_L - X_C = 0XL​−XC​=0
  1. Substitute into the impedance formula:
Z=R2+02=R2=RZ = \sqrt{R^2 + 0^2} = \sqrt{R^2} = RZ=R2+02​=R2​=R
  1. Therefore, the impedance of the circuit is
R\boxed{R}R​
  1. Checking options:
  • A: 2R22R^22R2 — incorrect (also dimensionally not impedance)
  • B: Zero — incorrect
  • C: RRR — correct
  • D: R2R\sqrt{2}R2​ — incorrect
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