When a coil is connected across a 20 V DC supply, it draws a current of 5 A. When it is connected across 20 V, 50 Hz AC supply, it draws a current of 4 A. The self-inductance of the coil is (Take = 3) _____ mH.

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Solution

Q.
When a coil is connected across a 20 V DC supply, it draws a current of 5 A. When it is connected across 20 V, 50 Hz AC supply, it draws a current of 4 A. The self-inductance of the coil is (Take $π$ = 3) _____ mH. [2024]

Ans.
(10)

$In DC circuit:$

$I = \frac{V}{R} (at steady state)$

$R = \frac{20}{5} = 4 Ω$

$In AC circuit:$

$I = \frac{V}{Z} \Rightarrow 4 = \frac{20}{\sqrt{R^{2} + {(L ω)}^{2}}}$

$16 + {(L ω)}^{2} = 25 \Rightarrow L ω = 3$

$L = \frac{3}{2 \times π \times f} = \frac{3}{2 \times 3 \times 50} = \frac{1}{100} = 10 mH$

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