# RLC CIRCUIT

Cuthbert Nyack The RLC circuit is shown schematically above.
The Impedance of the circuit is
Z = R + jwL + 1/jwC = R + j(wL - 1/wC)
The magnitude of the impedance of the circuit is given by:-
|Z| = Ö{R2 + (wL - 1/wC) 2 }
The phase of the impedance of the circuit is given by:-
Ðq = atan {(wL - 1/wC) /R}
The phase of the current and Vr is Ð-q.
Vc is delayed relative to Vr by 90° and Vl is advanced relative to Vr by 90°.

The magnitudes and phases of Vr (orange curve), Vc, (red curve) Vs (green curve) and Vl (blue curve) are shown by the sinusoidal waves in the applet above. The variation of the magnitudes and phases as a function of frequency and Q can be demonstrated by the applet. A frequency of 1 corresponds to the resonant frequency.

The above applet shows the magnitudes and phases of Vr, Vc and Vl represented in phasor form. The The sum of Vc and Vl and the parallelogram showing the resultant of Vl - Vc and Vr are shown by the purple lines. Note that at low frequencies most of the voltage appears accross the resistor while at higher frequencies the voltage is mostly accross the inductor.

The variation of the magnitudes of Vr, Vc and Vl is shown above as a function of frequency. The horizontal frequency scale goes from 0.5w o to 1.5wo. A plot of the phase of Vr is also shown. The vertical scale for phase varies from -p at the bottom to +p at the top. The magnitude of Vl-Vc is shown by the purple line.