RC Circuit

Series RC Circuit

In a series RC circuit, the current is the same through both the resistor and capacitor. Thus, the resistor voltage (U_R) is in phase with the current (I), and the capacitor voltage (U_C) lags the current by 90^o. Therefore, there is a phase difference of 90^o between U_R and U_C as shown above. From Kirchoff's voltage law, the sum of the voltage drops must equal the source voltage, U_s. Since U_R and U_C are 90^o out of phase, the magnitude of the source voltage can be expressed by using the Pythagorean theorem, as shown in the diagram.

Capacitive Impedance

The impedance Z of an RC circuit is the complete opposite to sinusoidal current. Its unit is the ohm. The phase angle is the phase difference between the total current and the source voltage. In a purely resistive circuit, the impedance is equal to total resistance. The phase angle is zero. In a purely capacitive circuit, the impedance is the total capacitive reactance. The phase angle is 90^o, with the current leading the voltage. The impedance, Z, of a series RC circuit, depends on both the R and the C reactance values. It is determined by the impedance triangle shown. The phase angle is between zero and 90^o.

Z_C Frequency Dependence

 

Capacitance reactance X_c varies inversely with frequency. Impedance Z changes in the same way as X_c. Therefore, in RC circuits, Z is inversely related to frequency. The diagram illustrates how Z and X_c change with frequency, with the source voltage held at a constant value. As the frequency increases, X_c decreases. Less voltage is dropped across the capacitor since U_c = I X_c. Also, Z decreases as X_c decreases, causing the current to increase. An increase in I causes more voltage across R as U_R = IR