Inductors & Capacitors in DC Circuits

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7 Οκτ 2013 (πριν από 4 χρόνια και 2 μήνες)

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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