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(C) When a soft iron core is inserted into the solenoid,its self-inductance $L$ increases because the permeability of the core material increases.The

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The bulb will become dimmer.

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(C) When a soft iron core is inserted into the solenoid,its self-inductance $L$ increases because the permeability of the core material increases.The inductive reactance of the solenoid is given by $X_L = \omega L$.As $L$ increases,the inductive reactance $X_L$ increases.The total impedance of the circuit is $Z = \sqrt{R^2 + X_L^2}$,where $R$ is the resistance of the bulb.Since $X_L$ increases,the total impedance $Z$ of the circuit increases.According to Ohm's law for $A.C.$ circuits,the current in the circuit is $I = \frac{V}{Z}$.As $Z$ increases,the current $I$ flowing through the circuit decreases.Since the brightness of the bulb depends on the power dissipated $(P = I^2 R)$,a decrease in current $I$ leads to a decrease in the brightness of the bulb. Therefore,the bulb will become dimmer.

$A$ bulb connected in series with an air-core solenoid is lit by an $A.C.$ source. If a soft iron core is inserted into the solenoid,then

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