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MHT CET 2024 (3 May, Shift 1) · Power, Power Factor & Wattless Current

Power, Power Factor & Wattless Current question from MHT CET 2024 (3 May, Shift 1)

Q30MHT CET 2024 · 3 MAY · SHIFT 1Easy

Power, Power Factor & Wattless Current

In an ACAC circuit E=200sin⁡(50t)E = 200\sin(50t) volt and I=100sin⁡(50t+π3) mAI = 100\sin\left(50t + \frac{\pi}{3}\right)\text{ mA}. The power dissipated in the circuit is

(sin⁡30∘=cos⁡60∘=0.5sin⁡60∘=cos⁡30∘=3/2)\left(\begin{matrix}\sin 30^\circ = \cos 60^\circ = 0.5 \\ \sin 60^\circ = \cos 30^\circ = \sqrt{3}/2\end{matrix}\right)

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Answer: (d)

  1. P=E0I02cos⁡ϕP = \frac{E_0I_0}{2}\cos\phi with ϕ=60∘\phi = 60^\circ
  2. P=200×0.12×0.5P = \frac{200\times0.1}{2}\times0.5
  3. P=5 WP = 5\text{ W}
  4. So the answer is (d) 5 watt.
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