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(B) For $DC$ supply,the coil acts as a pure resistor $R$. Given $V = 100 \ V$ and $I = 25 \ A$,the resistance is $R = \frac{V}{I} = \frac{100}{25} = 4

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$3$

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(B) For $DC$ supply,the coil acts as a pure resistor $R$. Given $V = 100 \ V$ and $I = 25 \ A$,the resistance is $R = \frac{V}{I} = \frac{100}{25} = 4 \ \Omega$.For $AC$ supply,the coil acts as an $LR$ circuit with impedance $Z$. Given $V = 100 \ V$ and $I = 20 \ A$,the impedance is $Z = \frac{V}{I} = \frac{100}{20} = 5 \ \Omega$.The impedance $Z$ is related to resistance $R$ and inductive reactance $X_L$ by the formula $Z^2 = R^2 + X_L^2$.Substituting the values,$5^2 = 4^2 + X_L^2$.$25 = 16 + X_L^2 \Rightarrow X_L^2 = 25 - 16 = 9$.Therefore,the reactance $X_L = \sqrt{9} = 3 \ \Omega$.

$A$ student connects a long air-cored coil of manganin wire to a $100 \ V$ $DC$ supply and records a current of $25 \ A$. When the same coil is connected across a $100 \ V, 50 \ Hz$ $AC$ supply,the current reduces to $20 \ A$. The reactance of the coil is $...... \Omega$.

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