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(A) When connected to a $D.C.$ source,the coil acts as a pure resistor because the frequency is zero.Using Ohm's law: $V = I R$$R = \frac{V}{I} = \fra

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$3$

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(A) When connected to a $D.C.$ source,the coil acts as a pure resistor because the frequency is zero.Using Ohm's law: $V = I R$$R = \frac{V}{I} = \frac{100}{25} = 4\, \Omega$When connected to an $A.C.$ source,the coil acts as an $LR$ circuit (resistor and inductor in series).The impedance $Z$ is given by: $Z = \frac{V}{I} = \frac{100}{20} = 5\, \Omega$The relationship between impedance,resistance,and inductive reactance is: $Z = \sqrt{X_{L}^{2} + R^{2}}$Squaring both sides: $Z^{2} = X_{L}^{2} + R^{2}$$5^{2} = X_{L}^{2} + 4^{2}$$25 = X_{L}^{2} + 16$$X_{L}^{2} = 25 - 16 = 9$$X_{L} = 3\, \Omega$Thus,the reactance of the coil is $3\, \Omega$.

$A$ 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 a $100\,V$,$50\,Hz$ $A.C.$ supply,the current reduces to $20\,A$. The reactance of the coil is....$\Omega $

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