Series Reactive RC Circuits
The voltage and current waveforms across a resistive element are ALWAYS in phase
The current is the same at each point in the circuit (series circuit)
The current and voltages across the capacitor are ALWAYS 90° out of phase ( iT leads vC )
The voltages across the resistor and capacitor are ALWAYS 90° out of phase
The amplitudes and phase relationships of the voltages and current depend on the values of
both the resistive and capacitive elements:
Purely Resistive Circuit
vS and iT are in phase
Purely Capacitive Circuit
iT leads vS by 90°
RC circuit
iT leads vS by an angle
determined by R and Xc
Impedance (Z)
Impedance in an AC circuit is the total opposition to the flow of current, and is given units of
ohms:
Z  R2  X C
2
The phase angle associated with a reactive RC circuit may be determined by the relative
magnitudes of the resistive and reactive elements:
 XC 

 R 
   tan 1 
Note: Impedance always has a phase angle associated with it
Complex Representation
Phasor Representation
Ohm’s Law in Series Reactive RC circuits
Since the voltage and current in a series RC circuit are out of phase, the phase angles MUST
be taken into account when solving these circuits. This is most easily accomplished by
representing phasor quantities in polar form. Substituting impedance (Z) for resistance gives
the following three equivalent forms of Ohm’s Law for reactive circuits:
V  IZ
I
V
Z
Z
V
I
where V, I and Z are phasor quantities (with both magnitude and phase angles)
Example: If the current in the following circuit is given as I  0.20mA , determine the
source voltage and draw a phasor diagram showing the relation between source voltage and
current.
KVL in Series Reactive RC Circuits
Since the voltages across the resistive and capacitive elements are NOT in phase, their
magnitudes CANNOT simply be added to find the total source voltage – they must always
be added as phasor quantities (magnitude and associated phase angle).
VS  VR  jVC
V 
2
2
VS  VR  VC   tan 1  C 
 VR 
The effects of frequency on a series reactive RC circuit
Remember that Capacitive Reactance is inversely proportional to frequency. Therefore, as
the frequency is increased, the capacitive reactance and therefore the total impedance
will decrease. The opposite is true if frequency is decreased – the capacitive reactance and
impedance both increase. The following figure illustrates the effect of frequency on total
circuit current and voltage across each component:
Since the phase angle associated with an AC RC circuit is determined by the ratio of Xc/R, it
follows that it is also inversely proportional to frequency:
Example: determine the current I, and the voltages across R and C in the following circuit.
Draw the phasor diagram showing all four components: