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JEE Main 2021 (25 Jul, Shift 2) · Power, Power Factor & Wattless Current

Power, Power Factor & Wattless Current question from JEE Main 2021 (25 Jul, Shift 2)

Q58JEE Main 2021 · 25 JUL · SHIFT 2Difficult

Power, Power Factor & Wattless Current

Two circuits are shown in the figure (a) & (b). At a frequency of ____________ rad/s the average power dissipated in one cycle will be same in both the circuits.

Figure

Numerical answer type. Work it out, then open the answer.

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Answer: 500

  1. Circuit (a): Pa=V2/RP_a = V^2/R. Circuit (b): Pb=I2R=V2R/Z2P_b = I^2R = V^2R/Z^2.
  2. Pa=PbP_a = P_b needs Z=RZ = R, i.e. resonance.
  3. ω=1LC=10.1×40×10−6=12×10−3\omega = \frac{1}{\sqrt{LC}} = \frac{1}{\sqrt{0.1\times 40\times10^{-6}}} = \frac{1}{2\times 10^{-3}}
  4. ω=500\omega = 500 rad/s
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