RLC Circuits Reactants

Running head: RLC CIRCUITS REACTANTS
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RLC CIRCUITS REACTANTS
Name
Institutional Affiliation

RLC CIRCUITS REACTANTS
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RLC CIRCUITS REACTANTS
Introduction
This experiment aims at familiarity with the components mentioned and how they
behave in a circuit when put together, either parallel or connected in series, and the circuit fed by
an alternating current.
Theory
The three basic passive components that are of focus are the resistance, inductance,
and capacitance which have distinct phase relationships among themselves when the circuitry is
of alternating supply that is sinusoidal in nature. When the resistor is alone in the circuit, the
waveform shall be in-phase with the current. When there is only an inductor the voltage wave
form is leading the current by 90O. When the circuit contain only capacitance, the wave
representing voltage shall be lagging the current by 90O. The reactive value produced by the
components mentioned above is what gives the phase differences. When the circuit is purely
resistive, only has resistance, the reactance is zero, it will be negative when the circuit is
capacitive and positive then the circuit is purely inductive. The table below shows a relationship
of the RLC circuit as described, only that this time there shall the impedance, which the table
shows how it relates to the other components as well (talked about in the next section)
Component
Resistor
(R)
Reactance
(X)
Impedance
(Z)
Resistor R 0 Z=R =R<0
Inductor 0 ωL
ZL = jωL =
ωL<+90
Capacitor 0 1/ωC
ZC=1/jωC
=1/ωC<-90
The impedance of the components
The three elements can be combined together and analysed, where they can be connected in
series or parallel, to form an RLC circuit. When analysing the RLC circuit, we shall need to take
into consideration the inductive, capacitive reactance and the resistances, XL, XC, and R
respectively. This will enable us to obtain the reactance of the circuit. Series RLC circuit are in a
class of 2nd order circuits since they store energy in two elements which are the capacitance and
inductance, see figure 1.

RLC CIRCUITS REACTANTS
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Figure 1: RLC circuit connected in series
There only one loop in the circuit of instantaneous current that flows through the loop, that
means the current flowing is the same for every component of the circuit. The inductive and
capacitive reactance of the circuit depends on the frequency at the supply, therefore the response
happening in sinusoidal way varies with the frequency. The voltage drops across individual each
element will be out of phase with one another.
i(t )=I max sin ( ωt ) ... ... ... ... ... ... ... ... ... ... ... ... ... ... ..(1)
Voltage across the resistor is written as VR shall be in phase with the current
Voltage across the inductor or inductive load, VL will be leading the current by 90O
The voltage across the capacitor or capacitive load shall lag the current by 90O
We can infer that VL and VC are 180O out of phase and opposite each other.
Figure 2:Circuits showing the waveforms and the circuit and how they relate
Considering all the parameters in place and considering the circuit given therein, we can have the
following equations:
For inductive reactance we have: X L=2 πfL=ωL