Consider a series RLC circuit with R = 15 Ohm, L = 204 mH C = 75 mu F, and a max

Question

Consider a series RLC circuit with R = 15 Ohm, L = 204 mH C = 75 mu F, and a maximum voltage of 146 V. (a) What is the impedance of the circuit at resonance? (b) What is the resonance frequency of the circuit? (c) When will the current be greatest: at resonance, at 10% below the resonant frequency or at 10% above the resonant frequency? The current is a maximum at resonance. The current is a maximum at 10% below the resonant frequency. The current is a maximum at 10% above the resonant frequency. (d) What is the rms current in the circuit at a frequency of 60 Hz?

Explanation / Answer

(d) here R = 15 ohm L = 204 mH = 0.204 H C = 75 uF = 75 x 10-6 F Vm = 146 volt

when f = 60 Hz

then XL = wL = 2.pie.f.L

XL = 2 x 3.14 x 60 x 0.204 = 76.8672 ohm

and XC = 1 / wC = 1 / (2.pie.f.C)

XC = 1 / ( 2 x 3.14 x 60 x 75 x 10-6 ) = 35.3857 ohm

so the impedence

Z2 = R2 + ( XL - XC ) 2

= (15)2 + ( 76.8672 - 35.3857 )2

= 1945.7148

Z = 44.1102 ohm

so the maximum current

Im = Vm / Z

= 146 / 44.1102 = 3.3098 Amp

so the RMS current

Irms = Im / root(2)

= 3.3098 / root(2) = 2.3404 Amp Ans

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