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JEE Main 20231 FebruaryMorning Shift
Exam
JEE Main
Year
2023
Date
1 February
Shift
Morning Shift
Subject
Physics
Chapter
Alternating Current

JEE Main 2023 · 1 February · Morning Shift · Physics · Alternating Current

A series LCR circuit is connected to an ac source of 220V, 50Hz ....

A series LCR circuit is connected to an ac source of 220V,50Hz220V, 50Hz. The circuit contain a resistance R=100ΩR = 100Ω and an inductor of inductive reactance XL=79.6Ω{X}_{L} = 79 . 6Ω. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be ______ μF\mu F.

Correct answer

0

Step-by-step solution

The average rate at which energy supplied i.e. power delivered is maximum in case of the resonance, therefore

XC=XL{X}_{C} = {X}_{L}

⇒1\omegaC=79.6Ω⇒ \dfrac{1}{\omegaC} = 79 . 6Ω

⇒C=1ω×79.6=12\pif×79.6=1100π×79.6=40μF⇒ C = \dfrac{1}{\omega \times 79 . 6} = \dfrac{1}{2\pif \times 79 . 6} = \dfrac{1}{100\pi \times 79 . 6} = 40\mu F

Hence, C=40μFC = 40\mu F.

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