Electromagnetic Induction and Alternating Current 7 Question 3

3. An arc lamp requires a direct current of $10 A$ at $80 V$ to function. If it is connected to a $220 V$ (rms), $50 Hz AC$ supply, the series inductor needed for it to work is close to

(2016 Main)

(a) $80 H$

(b) $0.08 H$

(c) $0.044 H$

(d) $0.065 H$

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Answer:

Correct Answer: 3. (d)

Solution:

  1. Resultant voltage, $V^{2}=V _R^{2}+V _L^{2} \Rightarrow 220^{2}=80^{2}+V _L^{2}$

Solving, we get

$$ \begin{aligned} V _L & \approx 205 V \\ X _L & =\frac{V _L}{I}=\frac{205}{10}=20.5 \Omega=\omega L \\ \therefore \quad L & =\frac{20.5}{2 \pi \times 50}=0.065 H \end{aligned} $$



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