For the series lcr circuit shown in the figure

Asked by admin @ 17/08/2021 in Physics viewed by 283 People

For the series LCR circuit shown in the figure, what is the resonance frequency and the amplitude of the current

at the resonating frequency8 mH220 V+ 20 uF44ohm

Answered by admin @ 17/08/2021

Answer:

2500 rad/s = 398 Hz

5 A

Explanation:

to find resonance Frequency

XL = XC

=> 2πfL = 1/2πfC

=> (2πf)² = 1/LC

=> 2πf = 1/√LC

L = 8 mH = 8 * 10⁻³

C = 20 μF = 20 * 10⁻⁶

2πf = 1/√LC

=> 2πf = 1/√(8 * 10⁻³ *20 * 10⁻⁶)

=> 2πf = 1/4 * 10⁻⁴

=> 2πf = 2500 rad/s

& f = 2500/2π = 398 Hz

Net Resistance at resonance frequency = 44 Ω

Voltage = 220V

Amplitude of current = 220/44 = 5 A

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