Then at resonance the above equation becomes. We remember that the total current flowing in a parallel RLC circuit is equal to the vector sum of the individual branch currents and for a given frequency is calculated as:Īt resonance, currents I L and I C are equal and cancelling giving a net reactive current equal to zero. Therefore at resonance the current flowing through the circuit must also be at its minimum as the inductive and capacitive branch currents are equal ( I L = I C ) and are 180 o out of phase. Then we have seen that the impedance of a parallel circuit at resonance is equivalent to the value of the resistance and this value must, therefore represent the maximum dynamic impedance ( Z d) of the circuit as shown.Īs the total susceptance is zero at the resonant frequency, the admittance is at its minimum and is equal to the conductance, G. So at the resonant frequency, ƒr the current drawn from the supply must be “in-phase” with the applied voltage as effectively there is only the resistance present in the parallel circuit, so the power factor becomes one or unity, ( θ = 0 o ).Īlso as the impedance of a parallel circuit changes with frequency, this makes the circuit impedance “dynamic” with the current at resonance being in-phase with the voltage since the impedance of the circuit acts as a resistance. Below the resonant frequency point, the inductive susceptance dominates the circuit producing a “lagging” power factor, whereas above the resonant frequency point the capacitive susceptance dominates producing a “leading” power factor. Then we can see that at the resonant frequency point were it crosses the horizontal axis the total circuit susceptance is zero. The final curve shows the plot of total susceptance of the parallel resonance circuit versus the frequency and is the difference between the two susceptance’s. The capacitive susceptance, B C is directly proportional to the frequency and is therefore represented by a straight line. From above, the inductive susceptance, B L is inversely proportional to the frequency as represented by the hyperbolic curve.

Define parallel