Capacitor In Series With Resistor

Introduction

In the DC analysis of resistor circuits nosotros examined how to calculate the total circuit resistance of series components. In this section we will use this approach to analyse circuits containing series resistors and capacitors. To do this we apply the capacitative reactance equally the effective 'resistance' of the capacitor then go along in a like manner to before.

Analysing Series RC Circuits

Y'all will recall that a series circuit provides only one road for the current to flow between two points in a circuit, then for instance the diagram below shows a resistor in serial with a capacitor betwixt the points A and B.

Series circuit

The total impedance (resistance) of this circuit is the contribution from both the capacitor and resistor. From the previous department nosotros have seen that the capacitative reactance Ninety is shifted by - 90° from the perturbing voltage signal and therefore is expressed in complex form as

The full circuit impedance is therefore

In ac analysis both the resistor and capacitor are treated equally phasor quantities, so Ninety is - 90° out of phase with respect to the resistor. Since Z is a phasor sum the result is presented on a phasor diagram (or complex plane)

Phasor diagram for Z

The magnitude of the impedance - the length of vector tin can be calculated using

For example if nosotros take the in a higher place circuit with a resistor of 100 Ω and Capacitor of 1x10-6 F and employ a sinusoidal voltage at a frequency of ten Hz, the capacitative reactance can be calculated every bit:

Xc = 1/(2 x 3.1415 10 10 ten 1x10-6) = fifteen.9x103 Ω

and so the total impedance in rectangular form is

Z = R - j Xc = 100 - j 15.9x103

We can convert this to polar form using the method above which gives a magnitude of xv.89x103 Ω and angle of -89.half dozen°. The magnitude is clearly dominated by the capacitors reactance since nosotros take considered a low operating frequency. Equally the frequency is altered the following response is observed (in phasor and bode forms)

Phase response for series circuit

The analysis of more than complex series circuits is carried out past summing the individual resistances and capacitative reactances into unmarried equivalent components then performing the same analysis as to a higher place