Question

A series RLC circuit has a resistance of 57.61 W, a capacitance of 13.13 mF, and an inductance of 196.03 mH. The circuit is connected to a variable-frequency sourcewith a fixed rms output of 23.86 V. If the source frequency is set at the circuit’s resonance frequency, what is the magnitude of the rms voltage across each of the circuit elements

Answer 1

Answer:

voltage across = 1.6 V

Explanation:

given data

resistance R = 57.61 Ω

capacitance c = 13.13 mF = 13.13 ×$10^{-3}$ F

inductance L = 196.03 mH = 0.19603 H

fixed rms output Vrms = 23.86 V

to find out

voltage across circuit

solution

we know resonant frequency that is

resonant frequency = 1 / ( 2π√(LC)

put the value

resonant frequency = 1 / ( 2π√(0.19603×13.13 ×$10^{-3}$)

resonant frequency f = 3.1370 HZ

so current will be at this resonant is

current = Vrms / R

current =  23.86 / 57.61

current = 0.4141 A

and

so voltage across will be

voltage across = current / ( 2π f C )

voltage across = 0.4141 / ( 2π ( 3.1370) 13.13 ×$10^{-3}$ )

voltage across = 1.6 V