For the same RLC series circuit having a 40.0 Ω resistor, a 3.00 mH inductor, and a 5.00 µF capacitor: (a) Find the resonant frequency. (b) Calculate Iᵣₘₛ at resonance if Vᵣₘₛ is 120 V. Ans ( (a) 1.30 kHz, (b) 3.00 A) 



Data Given:

Resistance of resistor = R =  40.0 Ω

Inductance of an inductor = L = 3.00 mH = 3.00 × 10⁻³ H

Capacitance of capacitor = C = 5.00 μF = 5.00 x10⁻⁶ F

Voltage (rms) = VrmsVrms = 120 V


To Find:

Resonant Frequency = f₀ = ?

Root Mean Square current at f₀  = IrmsIrms = ?


Solution:

The formula for resonant frequency is given by:

f₀ 12LC

by putting the corresponding values

f₀ 12×3.14163.00×10³H×5.0010F

f₀ 16.2831.5×10 Hz

f₀ 16.283×1.225×10 Hz

f₀ 17.695×10 Hz

f₀ = 0.12995 × 10⁴ Hz

or

f₀ = 1.2995 × 10³ Hz

or

f₀ 1.2995 kHz -------------------Ans. (1)


Since at resonance, the RLC circuit behaves like a pure resistive circuit and the impedance Z = R, So, the rms current is given by:

Irms VrmsR

by putting values

Irms 120V40Ω

Irms 3 A ----------------Ans. (2)


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