An inductor *L* of inductance *X _{L}* is connected in series with a bulb B and an ac source. How would brightness of the bulb change when (i) number of turn in the inductor is reduced, (ii) an iron rod is inserted in the inductor and (iii) a capacitor of reactance

*X*=

_{C}*X*is inserted in series in the circuit? Justify your answer in each case.

_{L}#### Solution

The inductive resistance (*X*_{L}) is given by

*X*_{L} = *ωL*

Where

*ω *= Angular frequency of ac source* L* = Inductance of the inductor

The net resistance of the circuit is given by

`Z=sqrt(X_(L^2)+R^2)`

where

*R* = Resistance of the bulb

(i) We know that if the number of turns in the inductor decreases, then inductance *L* decreases. So, the net resistance of the circuit decreases and, hence, the current through the circuit increases, increasing the brightness of the bulb.

(ii) If soft iron rod is inserted in the inductor, then the inductance* L* increases. Therefore, the current through the bulb will decrease, decreasing the brightness of the bulb.

(iii) If the capacitor of reactance *X*_{C} = *X*_{L} is connected in series with the circuit, then

`Z =sqrt((X_L-X_C)^2+R^2)`

⇒Z=R (∵X_{L}=X_{C})

This is a case of resonance. In this case, maximum current will flow through the circuit. Hence, the brightness of the bulb will increase