Inductors & Capacitors
in DC Circuits
EE291

Dr.Mohamed Abd

Elrahman
1
Inductors
•
An inductor is a coil of specific dimension used
to introduce specific amount of inductance to
a circuit
•
Inductance is the ability of an element to
oppose any sudden change in current
EE291

Dr.Mohamed
Abd

Elrahman
2
The inductance is calculated as follows:
L = (µ
0
. µ
r
. N
2
. A ) / l
Henry (H)
•
N is the number of turns of the coil
•
A is the cross section
•
l is the length of the coil
•
µ
0
is the permeability of air = 4
π
x 10

7
•
µ
r
is the relative permeability
EE291

Dr.Mohamed
Abd

Elrahman
3
EE291

Dr.Mohamed
Abd

Elrahman
4
Inductors
Transients in Inductive Networks
I) Storage Cycle
5
EE291

Dr.Mohamed
Abd

Elrahman
•
At the instant the switch is closed:
–
The inductance of the coil will prevent any sudden
change in current
–
The initial current will be zero
–
The voltage drop across the coil is V (supply
voltage)
–
The inductance at this case acts as an open circuit
•
Later,
–
The current will build up from zero and continue
to increase as follows:
i
L
= (E/R) . (1

e
–
t/
τ
)
such that
τ
= L/R
EE291

Dr.Mohamed
Abd

Elrahman
6
•
At the end of the storage cycle, the current
reaches E/R.
•
Thus, the coil acts as a short circuit
•
Increasing R, storage process is faster
EE291

Dr.Mohamed
Abd

Elrahman
7
E/R
i
L
t
II) Decay Cycle
EE291

Dr.Mohamed Abd

Elrahman
8
•
At the instant the switch is opened:
–
There should be a resistor R
2
to prevent spark
between switch terminals
–
The inductor will invert its terminal polarities to
act as a voltage source keeping the current in the
same direction
•
Later,
–
The current will decay from E/R
1
to zero according
to:
i
L
= (E/R
1
) . e
–
t/
τ
’
Such that
τ
’ = L/ (R
1
+R
2
)
EE291

Dr.Mohamed
Abd

Elrahman
9
•
At the end of the decay cycle, the current
reaches zero.
•
Thus, the coil acts as an open circuit
EE291

Dr.Mohamed
Abd

Elrahman
10
E/R1
Capacitors
•
A capacitor is an element constructed of two
parallel conducting plates separated by an
insulating material
•
Capacitance is a measure of a capacitor’s
ability to store charge on its plates
•
C= Q/V
farad
EE291

Dr.Mohamed
Abd

Elrahman
11
C =
ε
0
ε
r
(A / d)
•
ε
0
is the vacuum permittivity = 8.85 x 10

12
•
ε
r
is the relative permittivity
•
A is the area
•
d is the distance between the 2 plates
EE291

Dr.Mohamed
Abd

Elrahman
12
EE291

Dr.Mohamed
Abd

Elrahman
13
Transients in Capacitive Networks
EE291

Dr.Mohamed
Abd

Elrahman
14
1
2
I) Charging Cycle
•
At the instant the switch is at 1:
–
The initial current is E/R
–
The voltage drop across the resistor is V (supply
voltage)
–
The capacitance at this case acts as a short circuit
•
Later,
–
The current will decay during charging period as
follows:
i
ch
= (E/R) . (e
–
t/
τ
)
such that
τ
= R . C
EE291

Dr.Mohamed
Abd

Elrahman
15
•
At the end of the charging cycle, the current reaches
zero.
•
Thus, the capacitor is fully charged with the supply
voltage and acts as an open circuit
•
As R decreases, the charging time is faster
EE291

Dr.Mohamed
Abd

Elrahman
16
E/R
i
ch
EE291

Dr.Mohamed
Abd

Elrahman
17
1
2
II) Discharging Cycle
•
At the instant the switch is at 2:
–
The initial current is E/R
–
The voltage drop across the resistor is V (capacitor
voltage)
–
The capacitance at this case acts as a voltage
source that supplies current in opposite direction
•
Later,
–
The current will decay during charging period as
follows:
i
dis
= (E/R) . (e
–
t/
τ
)
such that
τ
= R . C
EE291

Dr.Mohamed
Abd

Elrahman
18
•
At the end of the discharging cycle, the current
reaches zero.
•
Thus, the capacitor has finished its charge and acts
as an open circuit
•
As R decreases, the charging time is faster
EE291

Dr.Mohamed
Abd

Elrahman
19
E/R
i
dis
Important Note
•
In a dc circuit, at steady state:
–
Any capacitor; replace with open circuit
–
Any inductor; replace with short circuit
EE291

Dr.Mohamed
Abd

Elrahman
20
•
See the lecture for more examples of DC
circuits with capacitors and inductors in steady
state.
EE291

Dr.Mohamed
Abd

Elrahman
21
EE291

Dr.Mohamed
Abd

Elrahman
22
20 V
200 micro F
Load (R=∞ ohm)
12 Volt to turn ON
Project
Design the network
the system should turn on after 10 sec of closing the switch
•
Assignment
–
Sheet 6
•
Small Project is to be delivered next week
23
EE291

Dr.Mohamed
Abd

Elrahman
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