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A series RLC circuit has components with the following values: L = 16.0 mH. C = 82.0 nF, R = 15.0 ohm, and Delta V_max = 100 V, with Delta v = Delta V_max sin omega t. Find the resonant frequency of the circuit. 4.3939e03 Resonance occurs when the impedance is at a minimum. kHz Find the amplitude of the current at the resonant frequency. 6.67 A Find the Q of the circuit. 2.68 How is the Q related to the capacitance, inductance and resistance? Find the amplitude of the voltage across the inductor at resonance. 9313.3 How is the potential across the capacitor is related to its reactance? kV

Answer 1

Given Data
         L = 16.0mH
           = 16.0*10^-3H
        C = 82 nF
           = 82*10^-9 F
        R = 15.0
       and V_max= 100 V

a) Resonant Frequency, fr = 1/(2*π*√(L*C))

   Resonant Frequency, fr = 1 / [2*π*√(16.0*10^-3*82*10^-9 )]

                                       ≈ 4394 Hz = 4.394 kHz

b) I max = V_max / R

I max = 100 / 15

              = 6.67 A

c) Q = L*ω₀ / R

Here ω₀ = 1/ √(LC)

ω₀ = 27608

Q = L*ω₀ / R

Q = (16.0*10^-3)*27608 / 15

         ≈ 29.45 Quality factor

d) V_L = X_L *I max

           = ω₀*L*Imax

           = (27608 )*(16.0*10^-3)*6.67

           ≈ 2946 V = 2.946 kV