719785-16-18P
AID: 20556 | 04/07/2016
The circuit has initial capacitor conditions
For t 0 , v 0 vs 12 volts
We have to convert the elements in the circuit from time domain to s-domain
Now convert the circuit elements for t 0
The input supply voltage is:
Thevenins Theorem
Thevenins Theorem
Thevenins Theorem
Thevenins Theorem
Thevenins Theorem
Thevenins Theorem
Thevenins theorem states that a
linear two-terminal circuit can
be replaced by an equivalent
circuit consisting of a voltage
source VTh in series w
719785-16-17P
AID: 20556 | 03/07/2016
The circuit has no initial capacitor conditions so, i 0 0 and v 0 0 0
Now convert the circuit from time domain to s-domain
We have to convert the elements in the circuit from time domain to s-domain
Apply the Lapl
719785-16-1P
AID: 20556 | 19/06/2016
Step 1 of 3
The current in an RLC circuit with second order differential equation is
d 2i
di
10 25i 0 . 1
2
dt
dt
di 0
The initial current conditions are i 0 7 A and
0
dt
Apply Laplace Transform to the equation (1)
719785-16-3P
AID: 20556 | 22/06/2016
Step 1 of 3
The voltage response in second order differential equation of RLC circuit is
d 2v
dv
2 v 0. 1
2
dt
dt
dv 0
The initial voltage conditions is v 0 350 V and
0
dt
Apply the Laplace Transform to the equation
719785-16-21P
AID: 20556 | 14/07/2016
From the circuit,
For t 0 sec, when the switch is at position A, the initial conditions for the voltage across
capacitor and current through inductor are:
V 0 2.5 4
Volts
V 0 10
And iL 0 0 Ampere
Applying KVL to the c
719785-16-2P
AID: 20556 | 19/06/2016
Step 1 of 3
The voltage in an RLC circuit with second order differential equation is
d 2v
dv
3 2 15 12v 0. 1
dt
dt
dv 0
V
The initial voltage conditions v 0 0 and
6
dt
s
Apply the Laplace Transform to the equation (1)
719785-16-19P
AID: 20556 | 07/09/2016
From the circuit,
For t 0 sec, when the switch is at position A, the initial conditions are: V 0 0 and
35
35
0.875 A
30 10 40
For t 0 sec, when the switch is in position B, we have a source-free RLC series circuit
719785-16-24P
AID: 20556 | 15/07/2016
From the circuit,
For
, switch is closed. The inductor acts as short circuit and the capacitor acts as open
t0
circuit. The equivalent circuit is as shown in figure below.
From this figure, the initial conditions for
719785-16-26P
AID: 20556 | 16/07/2016
From the circuit,
For t 0 sec, the switch is in position A, the inductor acts like a short circuit.
So, the initial conditions for the voltage across capacitor and current through inductor are:
Assume the initial volt
719785-16-7P
AID: 20556 | 22/06/2016
Step 1 of 3
The step response of an RLC circuit is
d 2i
di
2 5i 30. 1
2
dt
dt
The initial current conditions is i 0 18 A and
di 0
dt
36 A/s
Apply the Laplace Transform to the equation (1)
2
di 0
30
s I s si 0
2
719785-16-12P
AID: 20556 | 24/06/2016
Step 1 of 3
The RLC series circuit is applied with unit step voltage 8u t
Apply the Kirchhoffs voltage law (KVL) to the RLC series circuit
1
di
8u t Ri t idt L . 1
C
dt
The RLC circuit parameters is L 1 H, R 1 ohm, C
719785-16-25P
AID: 20556 | 16/07/2016
From the circuit,
By combining the resistors 15ohms, 25ohms which are connected in series then, the
equivalent resistance of
ohms is 40ohms. The equivalent value of 40ohms is
15
25
connected in parallel with 60ohms re
719785-16-23P
AID: 20556 | 15/07/2016
From the circuit,
For
, switch is closed. The inductor acts as short circuit and the capacitor acts as open
t0
circuit. The equivalent circuit is shown in figure (a).
From figure (a), the initial conditions for this c
719785-16-16P
AID: 20556 | 27/06/2016
The circuit initial capacitor current conditions are: i 0 0 and v 0 0 0
Now convert the circuit from time domain to s-domain
We have to convert the elements from time domain to s-domain
Apply the Laplace Transform
719785-16-9P
AID: 20556 | 24/06/2016
The current response of an series RLC circuit is:
d 2i t
di t i t
L
R
15 (1)
2
dt
dt
C
Substitute 0.5 H for L, 4 Ohms for R and 0.2 F for C
Substitute the initial current conditions is: i 0 7.5 A and
0
di 0
dt
Ap
Source Free RL Circuits
http:/172.16.1.41/vitcc/mod/resource/view.php?id=12930
Transient & Steady State Response
Transient Response
1. Switch Operation
Electrical circuits are connected to supply by closing the
switch and disconnected from the supply by o