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(D) The impedance of the $A.C.$ circuit is given by $Z = \sqrt{R^2 + X_L^2}$,where $X_L = \omega L = 2\pi f L$ is the inductive reactance.When an iron

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an iron rod is inserted in the coil.

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(D) The impedance of the $A.C.$ circuit is given by $Z = \sqrt{R^2 + X_L^2}$,where $X_L = \omega L = 2\pi f L$ is the inductive reactance.When an iron rod is inserted into the coil,the permeability of the core increases,which significantly increases the self-inductance $L$ of the coil.As $L$ increases,the inductive reactance $X_L = 2\pi f L$ increases.Consequently,the total impedance $Z = \sqrt{R^2 + X_L^2}$ of the circuit increases.Since the current in the circuit is $I = V/Z$,an increase in $Z$ leads to a decrease in the current $I$ flowing through the bulb.As the brightness of the bulb is proportional to $I^2 R$,a decrease in current results in a decrease in the brightness of the bulb.

$A$ coil of self-inductance $L$ is connected in series with a bulb $B$ and an $A.C.$ source. Brightness of the bulb decreases when

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