Introduction to Electric Circuits

6 Resonance

6.1 SERIES RESONANCE

We saw in Chapter 4 that under certain conditions a series RLC circuit such as

that shown in Fig. 6.1 behaves as a pure resistance. This happens when the

inductive reactance XL (=2-rrfL) is equal to the capacitive reactance

Xc (= 1/2"rrfC). The circuit impedance, Z (=~[R 2 + (XL -- Xc)2]) then becomes

equal to R since XL -- Xc - 0. This condition is called series resonance and has

important applications in filter circuits and radio and television tuning circuits.

Figure 6.1

I R

VR

vl

i

L C

VL VC

The phasor diagram, drawn for the condition when XL- Xo is given in

Fig. 6.2 and this is drawn using the current I as the reference phasor.

Figure 6.2

VL~

Vc ~

MR

r I (reference)

9 The voltage phasor VL = IXL is drawn 90 ~ ahead of the current phasor.

9 The voltage phasor Vc = IXc is drawn 90 ~ behind the current phasor.