##### From Network Analysis and Circuits

**12.3 PHASOR DIAGRAM OF SERIES RLC CIRCUIT**

The nature of the phasor diagram of a series RLC circuit depends on the

frequency *f* of the applied signal in relation to the frequency of resonance *f*_{0}.

Three different cases may be considered:

* (i) f = f _{r}, (ii) f < f_{r}, and (iii) f > f_{r}. *

with *f = f _{0}*, the reactance X

_{L}of inductor L equals the reactance

of capacitor C.

The circuit is then purely resistive and the voltage V across the circuit is

in phase with the current I. The phasor diagram for the series RLC circuit

of Figure 12.4 for the series resonance condition is shown in Figure 12.4(*a*).

*(a ) f = f _{r} (b) f < f_{r}*

*(c) f > f*

_{r}* FIGURE 12.4 Phasor diagram of the series RLC circuit.*

With *f < f _{r}*, the negative reactance X

*of capacitor C exceeds the positive*

_{c}reactance X

_{L}of inductor L. Hence, the overall reactance is capacitive.

Current I leads the applied voltage V.

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