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:
- Resultant voltage, $V^{2}=V _R^{2}+V _L^{2} \Rightarrow 220^{2}=80^{2}+V _L^{2}$
Solving, we get
$$ \begin{aligned} V _L & \approx 205 V \\ X _L & =\frac{V _L}{I}=\frac{205}{10}=20.5 \Omega=\omega L \\ \therefore \quad L & =\frac{20.5}{2 \pi \times 50}=0.065 H \end{aligned} $$
