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A student connects a long air cored–coil of Manganin wire to a 100 V D.C. supply and records a current of 25 A. When the same coil is connected across 100 V-50 Hz A.C. the current reduces to 20 A. The reactance of the coil is

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$3 Ω$

$4 Ω$

$6 Ω$

$5 Ω$

answer is B.

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Detailed Solution

$i_{DC} = ε / R \Rightarrow R = \frac{100}{25} = 4 Ω$

$i_{AC} = ε / Z \Rightarrow Z = \frac{100}{20} = 5 Ω$

$Z = \sqrt{R^{2} + {X_{L}}^{2}}$

$\Rightarrow X_{L} = 3 Ω$

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