Electrical circuits lecture notes b. Tech

 
Element Impedance: 
Circuit element 
Resistsnce(R) 
Reactance(X) 
Impeadance(Z) 
RESISTOR 
R 
0 
Z
R
=R RL0
0 
INDUCTOR 
L 
WL 
Z
L
=WL L90
0 
CAPACITOR 
C 
1/WC 
Z
C
=1/WC L-90
0 
The series RLC circuit above has a single loop with the instantaneous current flowing 
through the loop being the same for each circuit element. Since the inductive and capacitive 
reactance’s X
L
and X
C
are a function of the supply frequency, the sinusoidal response of a 
series RLC circuit will therefore vary with frequency, ƒ. Then the individual voltage drops 
across each circuit element of R, L and C element will be “out-of-phase” with each other as 
defined by: 
i
(t)
= I
max
sin(ωt)
The instantaneous voltage across a pure resistor, V
R
is “in-phase” with current
The instantaneous voltage across a pure inductor, V
L
“leads” the current by 90
o
The instantaneous voltage across a pure capacitor, V
C
“lags” the current by 90
o
Therefore, V
L
and V
C
are 180
o
“out-of-phase” and in opposition to each other 
The amplitude of the source voltage across all three components in a series RLC circuit is 
made up of the three individual component voltages, V
R
, V
L
and V
C
with the current common 
to all three components. The vector diagrams will therefore have the current vector as their 
reference with the three voltage vectors being plotted with respect to this reference as shown 
below. 
Individual Voltage Vectors 

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This means then that we cannot simply add together V
R
, V
L
and V
C
to find the supply 
voltage, V
S
across all three components as all three voltage vectors point in different 
directions with regards to the current vector. Therefore we will have to find the supply 
voltage, V
S
as the Phasor Sum of the three component voltages combined together 
vectorially. 
Kirchoff’s voltage law ( KVL ) for both loop and nodal circuits states that around any closed 
loop the sum of voltage drops around the loop equals the sum of the EMF’s. Then applying 
this law to the these three voltages will give us the amplitude of the source voltage, V
S
as.