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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 $x ω .$ 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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