The frequency response of this type of circuit is shown below in phasor and bode forms. Now we will examine the response of a circuit as above with a capacitative reactance of 50 Ω and a resistance of 100 Ω Z = 100 x 50/(100 2 + 50 2)½ = 44.7°Īnd the angle is -63.4°. Treating R2 above as the capacitative reactance and a little bit of complex number algebra we can show that the impedance magnitude and phase angle is given by the following You will recall that the rule for summing resistors in parallel is given by 1/RT = 1/R1 + 1/R2 Then we use the same rules introduced for summing resistors in series remembering that now we are dealing with phasor quantities. To calculate the total impedance (resistance) of this circuit we again use the capacitative reactance Xc as the equivalent resistance of the capacitor. The figure below shows a parallel combination of a single resistor and capacitor between the points A and B. As with the previous section we can use the DC analysis of resistor parallel circuits as a starting point and then account for the phase relationship between the current flowing through the resistor and capacitor components.Īs we have seen previously in a parallel circuit the current has a number of alternative pathways to follow and the route taken depends upon the relative 'resistance' of each branch. In this final section we examine the frequency response of circuits containing resistors and capacitors in parallel combinations.
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