JEE MAIN - Physics (2016 (Offline) - No. 6)
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 :
0.044 H
0.065 H
80 H
0.08 H
Explanation
From the circuit, we have
_en_6_1.png)
$$R = {{80} \over {10}} = 8\,\Omega $$
$$10 = {{220} \over {\sqrt {{R^2} + X_L^2} }} \Rightarrow \sqrt {64 + X_L^2} = 22$$
$$ \Rightarrow X_L^2 = 484 - 64 = 420$$
$$ \Rightarrow {X_L} = \sqrt {420} = 20.5\,\Omega $$
$$ \Rightarrow \omega L = 20.5$$
$$L = {{20.5} \over {2\pi \times 50}} = {{20.5} \over {314}} = 0.065\,H$$
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