Question

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

220 V
+ 20 uF
44ohm​

Answer 1

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

Answer 2

Answer:

see the attached image