3
Al-Mustaqbal University College http://www.mustaqbal-college.edu.iq/
The analysis of a series RLC circuit is the same as that for the series RL and RC circuits we
looked at previously, except this time we need to consider the magnitudes of both X
L
and
X
C
to find the overall circuit reactance. Series RLC circuits are classed as second-order
circuits because they contain two energy storage elements, an inductance L and a
capacitance C. Consider the RLC circuit below. The phasor diagram for a series RLC circuit
is produced by combining the three individual phasors above and adding these voltages
vectorially. Since the current flowing through the circuit is common to all three circuit
elements, we can use this as the reference vector with the three voltage vectors drawn
relative to this at their corresponding angles.
The resulting vector V
S
is obtained by adding together two of the vectors, V
L
and V
C
and
then adding this sum to the remaining vector V
R
. The resulting angle obtained between V
S
and I will be the circuits phase angle as shown below.
We can see from the phasor diagram in Fig. 2 above that the voltage vectors produce a
rectangular triangle, comprising of hypotenuse V
S
, horizontal axis V
R
and vertical axis V
L
– V
C
. We notice that this forms our old favourite the Voltage Triangle and we can therefore
use Pythagoras’s theorem on this voltage triangle to mathematically obtain the value of V
S
as shown. The voltage triangle for a series RLC Circuit: