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Q.

Two identical inductors each of inductance L are connected in series and then a capacitor of capacitance C is connected in parallel to one of the inductors.
This combination is connected across a series combination of an incandescent lamp and a variable frequency alternating voltage source as shown in the figure. It has been observed that the lamp glows with minimum brightness at an angular frequency $ω$ .
Angular frequency that will make the lamp glow with maximum brightness is $x ω .$ Find x?

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answer is 1.41.

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Detailed Solution

$Z = \frac{j ω L}{1 - ω^{2} L C} + j ω L + R Z = \sqrt{R^{2} + ω^{2} L^{2} {(\frac{1 - ω^{2} L C}{1 - ω^{2} L C})}^{2}}$

for max (or) min Z
differentiating $ω L (\frac{2 - ω^{2} L C}{1 - ω^{2} L C})$ w.r.t. $ω$ .
we get $ω_{1} = \sqrt{2} ω_{2}$

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Two identical inductors each of inductance L are connected in series and then a capacitor of capacitance C is connected in parallel to one of the inductors.This combination is connected across a series combination of an incandescent lamp and a variable frequency alternating voltage source as shown in the figure. It has been observed that the lamp glows with minimum brightness at an angular frequency ω. Angular frequency that will make the lamp glow with maximum brightness is xω. Find x?