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1. Chameli Devi Group of
Institution
Project Title :- Response of AC Voltage across Series Resistive, Inductive,
Capacitive Circuit.
Subject :- Basic Electrical & Electonics Engineering(BT104)
Submitted by :- Pranjal Vani, Piyush Gupta, Prashant Chouhan, Priyansh Mishra,
Payal Solanki
Submitted to :- Aashish Shrivastav

2. Alternating Current
• An alternating function or AC Waveform on the other hand is defined as one
that varies in both magnitude and direction in more or less an even manner
with respect to time making it a “Bi-directional” waveform. An AC function
can represent either a power source or a signal source with the shape of
an AC waveform generally following that of a mathematical sinusoid being
defined as: A(t) = Amax*sin(2πƒt).
• The term AC or to give it its full description of Alternating Current, generally
refers to a time-varying waveform with the most common of all being called
a Sinusoid better known as a Sinusoidal Waveform. Sinusoidal waveforms are
more generally called by their short description as Sine Waves. Sine waves
are by far one of the most important types of AC waveform used in electrical
engineering.

3. Series RLC Circuit Analysis
• Series RLC circuits consist of a resistance, a capacitance and an
inductance connected in series across an alternating supply.
• Thus far we have seen that the three basic passive components
of: Resistance, Inductance, and Capacitance have very different phase
relationships to each other when connected to a sinusoidal
alternating voltage. But we can connect these passive elements
together to form a series RLC circuit in series with an applied voltage
supply.

5. 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 XL and XC 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) = Imax sin(ωt)
• The instantaneous voltage across a pure resistor, VR is “in-phase” with current
• The instantaneous voltage across a pure inductor, VL “leads” the current by 90o
• The instantaneous voltage across a pure capacitor, VC “lags” the current by 90o
• Therefore, VL and VC are 180o “out-of-phase” and in opposition to each other.
For the series RLC circuit above, this can be shown as:

6. Impedance
• The impedance of an ideal capacitor is equal in magnitude to its
reactance, but these two quantities are not identical. Reactance is
expressed as an ordinary number with the unit ohms, whereas the
impedance of a capacitor is the reactance multiplied by -j, i.e., Z = -jX.
• Impedance, represented by the symbol Z, is a measure of the
opposition to electrical flow. It is measured in ohms. For DC systems,
impedance and resistance are the same, defined as the voltage across
an element divided by the current (R = V/I).

7. Phasor Diagram
• Phasor Diagrams are a graphical way
of representing the magnitude and
directional relationship between two
or more alternating quantities.
• Phasor diagrams present a graphical
representation, plotted on a
coordinate system, of the phase
relationship between the voltages and
currents within passive components
or a whole circuit. Generally, phasors
are defined relative to a reference
phasor which is always points to the
right along the x-axis.

8. Resonance
• Resonance occurs in a series circuit when the supply frequency
causes the voltages across L and C to be equal and opposite in phase.
• A resonant circuit consists of R, L, and C elements and whose
frequency response characteristic changes with changes in frequency.
In this tutorial we will look at the frequency response of a series
resonance circuit and see how to calculate its resonant and cut-off
frequencies.

9. Frequency Response
• It is a plot of the magnitude of
the output Voltage of a
resonance circuit as function of
frequency. The response of
course starts at zero, reaches a
maximum value in the vicinity of
the natural resonant frequency,
and then drops again to zero as
ω becomes infinite.

10. Time Domain Response
• The time domain response of a series RLC circuit refers to the
behavior of voltage and current over time.
• It includes both the transient response which settles down over time
and the steady state response which remains constant.
• The time constants, damping and oscillations affects the response of
the circuit.

11. Applications
• Series RLC circuits find the application in various fields.
• They are used in signal processing filtering, frequency selection,
impedance matching and resonance based systems.
• Example includes radio receivers, audio amplifiers and power factor
correction circuits.