Phasor Diagram of Series RLC Circuit
The phasor diagram of series RLC circuit is drawn by combining the phasor diagram of resistor, inductor
and capacitor. Before doing so, one should understand the relationship between voltage and current in
case of resistor, capacitor and inductor.
1. Resistor - In case of resistor, the voltage and the current are in same phase or we can
say that the phase angle difference between voltage and current is zero.
2. Inductor - In inductor, the voltage and the current are not in phase. The voltage leads
that of current by 90° or in the other words, voltage attains its maximum and zero value
90° before the current attains it.
3. Capacitor - In case of capacitor, the current leads the voltage by 90° or in the other
words, voltage attains its maximum and zero value 0° after the current attains it i.e the
phasor diagram of capacitor is exactly opposite of inductor.
NOTE: For remembering the phase relationship between voltage and current, learn this simple word
called 'CIVIL', i.e in capacitor current leads voltage and voltage leads current in inductor.
RLC circuit - For drawing the
phasor diagram of series RLC circuit, follow these steps:
Step - I. In case of series RLC circuit; resistor, capacitor and inductor are connected in series; so, the
current flowing in all the elements are same i.e I r = Il = Ic = I. For drawing the phasor diagram, take
current phasor as reference and draw it on horizontal axis as shown in diagram. Step - II. In case of
resistor, both voltage and current are in same phase. So draw the voltage phasor, VR along same axis or
direction as that of current phasor i.e VR is in phase with I.
Step - III. We know that in inductor, voltage leads current by 90° so draw Vl (voltage drop across
inductor) perpendicular to current phasor in leading direction.
Step - IV. In case of capacitor, the voltage lags behind the current by 90° so draw Vc (voltage drop across
capacitor) perpendicular to current phasor in downwards direction.
Step - V. For drawing the resultant diagram, draw Vc in upwards direction. Now draw resultant, Vs which
and
VL
VC.
is
vector
sum
of
voltage
Vr
Impedance for a Series RLC Circuit
The impedance Z of a series RLC circuit is defined as
opposition to the flow of current, due to circuit resistance R, inductive reactance, XL and capacitive
reactance, XC. If the inductive reactance is greater than the capacitive reactance, i.e XL > XC, then the RLC
circuit has lagging phase angle and if the capacitive reactance is greater than the inductive reactance, i.e
XC > XL then the RLC circuit have leading phase angle and if both inductive and capacitive are the same,
i.e XL = XC then circuit will behave as purely resistive circuit.
We know that,
Substituting the values VS2 = (IR)2 + (I XL - I XC )2
From this impedance triangle: by using Pythagoras theorem we get;
Variation in Resistance, Reactance and Impedance with Frequency
In
circuit, three types of impedance are involved-
series
RLC
4. Electrical resistance - Resistance is independent of frequency, so it remains constant
with change in frequency.
5. Inductive reactance, XL - We know that XL = 2πfL so, inductive reactance varies directly
with frequency. So the graph between frequency and inductive reactance is a straight
line passing through the centre as shown by curve a.
6. Capacitive reactance, XC - From the formula of capacitive reactance, XC = 1/ 2πfC so,
capacitive reactance varies inversely with frequency. Since the net reactance is ( XL - XC).
So for drawing curve of ( XL - XC), firstly draw the graph of ( -XC) which is shown by curve
b and then draw a curve for net reactance which is shown as curve c.
7. The total impedance of circuit is shown by curve d which is obtained by adding constant
resistor value to the net reactance.