The Impedance Triangle for a Series RLC Circuit

These circuit impedance’s can be drawn and represented by an Impedance Triangle as shown below. This will give us the RLC circuits overall impedance, Z. The Impedance of a Series RLC CircuitĪs the three vector voltages are out-of-phase with each other, X L, X C and R must also be “out-of-phase” with each other with the relationship between R, X L and X C being the vector sum of these three components. Thus the total impedance of the circuit being thought of as the voltage source required to drive a current through it.

Then in the series RLC circuit above, it can be seen that the opposition to current flow is made up of three components, X L, X C and R with the reactance, X T of any series RLC circuit being defined as: X T = X L – X C or X T = X C – X L whichever is greater. This proportionality constant is called the Impedance of the circuit which ultimately depends upon the resistance and the inductive and capacitive reactance’s. So we can see that the amplitude of the source voltage is proportional to the amplitude of the current flowing through the circuit. Series RLC circuits are classed as second-order circuits because they contain two energy storage elements, an inductance L and a capacitance C. The analysis of a series RLC circuit is the same as that for the dual series R L and R C circuits we looked at previously, except this time we need to take into account the magnitudes of both X L and X C to find the overall circuit reactance. Instead of analysing each passive element separately, we can combine all three together into a series RLC circuit. This Phase Difference, Φ depends upon the reactive value of the components being used and hopefully by now we know that reactance, ( X ) is zero if the circuit element is resistive, positive if the circuit element is inductive and negative if it is capacitive thus giving their resulting impedances as: Element Impedance Circuit Element In a pure capacitance the voltage waveform “lags” the current by 90 o, giving us the expression of: ICE. In a pure inductance the voltage waveform “leads” the current by 90 o, giving us the expression of: ELI. In a pure ohmic resistor the voltage waveforms are “in-phase” with the current. But we can connect these passive elements together to form a series RLC circuit in series with an applied voltage supply. Thus far we have seen that the three basic passive components of: Resistance, Inductance, and Capacitance have very different phase relationships to each other when connected to a sinusoidal alternating voltage.

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