Solved Problems: Resonance and Coupled Circuits

Q. A pure inductance of 150 mH is connected in parallel with a 40 μF capacitor across a 50 V, variable frequency supply. Determine (a) the resonant frequency of the circuit and (b) the current circulating in the capacitor and inductance at resonance.

The circuit diagram is shown in Figure 16.10.

(a)   Parallel   resonant-R/L frequency,  

However, resistance R = 0. Hence,

fr   =   1/2π√1/LC

= 64.97 Hz

(b) Current circulating in L and C at resonance, ICIRC = V/XC

=           V   /1/2πfrC

=           2πfrCV

Alternatively, ICIRC = V/XL

=           V/2πfrL

=           50/2π64.9*0.15

= 0.817 A

Q. 1- A series L–R–C circuit has a sinusoidal input voltage of maximum value 12 V.  If inductance, L = 20 mH, resistance, R = 80 Ω, and capacitance, C = 400 nF,  determine (a) the resonant frequency, (b) the value of the p.d. across the  capacitor at the resonant frequency, (c) the frequency at which the p.d. across  the capacitor is a maximum, and (d) the value of the maximum voltage across the capacitor.

Q- A coil of inductance 5 mH and resistance 10 Ω is connected in parallel with a  250 nF capacitor across a 50 V variable-frequency supply. Determine (a) the  resonant frequency, (b) the dynamic resistance, (c) the current at resonance, and (d) the circuit Q-factor at resonance.

Summary of the properties of RLC resonant circuits.

Series Resonance

The basic series-resonant circuit is shown in fig. 1. Of interest here in how the steady state amplitude and the phase angle of the current vary with the frequency of the sinusoidal voltage source. As the frequency of the source changes, the maximum amplitude of the source voltage (Vm) is held constant