RC circuit, Phasors and Frequency Response.

Cuthbert Nyack

The basic series RC circuit is shown schematically below.

The total impedance of the circuit can be written as:- Z = R + 1/jwC = R - j/wC
The impedance can be represented as a magnitude and a phase with the magnitude of the impedance given by:-
|Z| = Ö {R² + 1/w²C²}
and the phase of the impedance given by:-
Ðq = atan { -1/(wCR)}

The Capacitor voltage/Input voltage = 1/(1 + jwCR) with phase atan { -wCR).

The Resistor voltage/Input voltage = jwCR/(1 + jwCR) with phase p/2 - atan {wCR).
The Resistor voltage leads the Capacitor voltage by p/2.

The applet below illustrates the frequency response shown as a Bode plot and as a variation of phasor magnitude and phase.

Fn = 0 in the applet shows the frequency variation of the magnitude and phase of the voltages across the capacitor and resistor. Numerical values can be seen by changing B/L.

Fn = 1 shows the Phasor variation with frequency w. T = RC is the time constant of the RC circuit.
eg parameters(1.0, 1.0, na, na, na, na, 0 or 1, 375, na, 1.5) show the capacitor and resistor voltages both down by 3dB at 1rad/s, the phase of the resistor voltage is ~+45° and that of the capacitor is ~-45°. Numerical values are shown on the plot. "na" above means not applicable.

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