Transients are momentary surges or spikes in electric currents and voltages that are induced upon power lines. They are characterized by extremely high voltages that drive tremendous amounts of current for brief periods of time. Transients occur in circuits containing energy storage elements like inductors or capacitors, which cannot instantly change the stored energy. Differential equations are used to analyze and study circuit responses under transient conditions. First-order circuits contain a single energy storage element, while second-order circuits contain both an inductor and capacitor. The time constant of an RL circuit is the time required for the current to reach approximately 63% of its final steady-state value.

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2. Introduction of Transient.
Type of Transient.
Importance of Differential Equation in Transient.
Transient in RL circuit (DC). Short circuit current, Time constant.

3. What are Transients?
Introduction
Transients are the surges or spikes in electric currents and voltages
which are transmitted through power or data lines.
Electrical transients are momentary bursts of energy induced upon
power, data, or communication lines. They are characterized by
extremely high voltages that drive tremendous amounts of current into
an electrical circuit for a few millionths, up to a few thousandths, of a
second.
A stage in which variations are created is called transient stage.

4. Transient Analogy(for understanding)
 Its analogy can be compared with bucket of water in which
water is in its normal state but when a water is touched it create
some waveforms or disturbances (which are similar to
transient)and after sometime disturbances will end and then
water will be in its normal steady state as it was before.

5. Presence of Transient
Its Important to note that The transient part will not present in
the response of an electrical circuit or network, if it contains only
resistances. Because resistor is having the ability to adjust any
amount of voltage and current.
The transient part occurs in the response of an electrical circuit
or network due to the presence of energy storing elements such
as inductor and capacitor. Because they can’t change the energy
stored in those elements instantly.

6. Types of Transient
Types Of Transient
On the basis of Energy storing devices.
Single-energy Transient: These transients are those in which
only one form of energy, either electromagnetic or electrostatic
is involved as in R-L and R-C circuits.
Double Energy Transient: These transients are those in which
both electromagnetic or electrostatic is involved as in R-L-C
circuits.

7. (a)Initiation Transients : These are produced when a circuit, which is
originally dead, is energized.
(b)Subsidence Transients : These are produced when an energized
circuit is rapidly de-energized and reaches an eventual steady-stage of
zero current or voltage, as in the case of short-circuiting an R-L or R-C
circuit suddenly.
(c)Transition Transients : These are due to sudden but energetic
changes from one steady state to another.
Classification of Transient

8. (a)Complex Transients : These are produced in a circuit which is
simultaneously subjected to two transients due to two independent
disturbances or when the disturbing force producing the transients is
itself variable.
(b)Relaxation Transients : In these transients, the transition occurs
cyclically towards states, which when reached, become unstable
themselves.

9. Order of Transient
Some of the important differential equations, used in the treatment of
single and double energy transients, are given below. We will consider
both first-order and second-order differential equations.
1.First Order Equations
2.Second Order Equations

10. First Order Differential Equation
 Any circuit with a single energy storage element, an number
of sources, and an arbitrary number of resistors is a circuit of
first order.
 RL or RC circuit are example of First order transient.

11. Second Order Differential Equation
 Any circuit with a single capacitor, a single inductor, an arbitrary number of
sources, and an arbitrary number of resistors is a circuit of second order.
 RLC circuit is an example of Second order transient equation.

13. A First-Order RC Circuit
 One capacitor and one resistor in series
 The source and resistor may be equivalent to a circuit with many resistors
and sources
Lect12 EEE 202 13
R
Cvs(t)
+
–
vc(t)
+ –
vr(t)
+
–

14. A First-Order RL Circuit
 One inductor and one resistor in parallel
 The current source and resistor may be equivalent to a circuit with many
resistors and sources
Lect12 EEE 202 14
v(t)is(t) R L
+
–

15. A Second Order RLC Circuit
 The source and resistor may be equivalent to a circuit with many resistors
and sources
 As seen In the circuit below capacitor, Inductor are involved.
Lect12 EEE 202 15
vs(t)
R
C
i (t)
L
+
–

16. )()(...
)()(
01
1
1 tftxa
dt
txd
a
dt
txd
a n
n
nn
n
n  



17. Importance
 Differential Equation is used to analyze and study the response of circuit
when subjected to transient.
 Every voltage and current is the solution to a differential equation.

18. The Differential Equation
 Every voltage and current is the solution to a differential equation
 In a circuit of order n, these differential equations have order n
 The number and configuration of the energy storage elements determines
the order of the circuit
 n  number of energy storage elements
Lect12 EEE 202 18

19. The Differential Equation
 Equations are linear, constant coefficient:
 The variable x(t) could be voltage or current
 The coefficients an through a0 depend on the component values of
circuit elements
 The function f(t) depends on the circuit elements and on the sources
in the circuit
Lect12 EEE 202 19
)()(...
)()(
01
1
1 tftxa
dt
txd
a
dt
txd
a n
n
nn
n
n  



21. Transients in RL Circuit(DC)
 A LR Series Circuit consists basically of an
inductor of inductance, L connected in series
with a resistor of resistance, R. The resistance
“R” is the DC resistive value of the wire turns or
loops that goes into making up the inductors
coil. Consider the LR series circuit below.

22.  The current, i begins to flow through the circuit but does not rise rapidly
to its maximum value of Imax as determined by the ratio of V / R (Ohms
Law).
 This limiting factor is due to the presence of the self induced emf within
the inductor as a result of the growth of magnetic flux, (Lenz’s Law).

23.  Kirchhoff’s voltage law (KVL) gives us:




26. Time Constant
 The Time constant is time
Required for transient to
decrease to zero.
 The time required for the
current flowing in the LR
series circuit to reach its
maximum steady state value
is equivalent to about 5 time
constants or 5τ.

27. T H E E N D
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