Capacitor and
Inductor
Ch. 6 – Inductance and Capacitance

Inductors store magnetic energy

The unit of inductance is the Henry (H)

The current flows to an inductance can not change rapidly
i(0 )  i(0 )

Capacitors store electric energy

The unit f capacitance is the Farad (F)

The voltage across a capacitor can not change rapidly
v(0 )  v(0 )
ELEC 250 – Summer 2015
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Ch. 6 – Inductance and Capacitance
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Inductors

Inductance plays a role in mediating the change of current
that passes through it.
t
di
v(t) = L
dt
1
i (t )   v d  i (0)
L0
Power of Inductor
Energy of Inductor
di
P  Li
dt
1 2
w  Li
2
ELEC 250 – Summer 2015
Ch. 6 – Inductance and Capacitance
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Example:
Q1. The current and the voltage across a 10 H inductor are
known to be zero for t  0 . The voltage across the
inductor is given by the graph in the following figure
for t  0 .
Derive expression of current versus time for 0  t  75ms ?
t
0  t  25 ms  v  800t
1
x2 t
 i   800 x dx  0  80 |0
10 0
2
 i  40t 2
25 ms  t  75 ms 
initial current value :
i(0.025)  25 mA
t
 v  20
1
t
 i
20
x
dx

0.025

2
x
|
0.025 +0.025  i  2t  0.025

10 0.025
ELEC 250 – Summer 2015
Ch. 6 – Inductance and Capacitance
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Capacitors

The current through a capacitor and the voltage across it
are given as
t
dv
i(t )  C
dt
1
v(t )   i d  v(0)
C0
Power of Capacitor
Energy of Capacitor
1 2
w  Cv
2
dv
P  Cv
dt
ELEC 250 – Summer 2015
Ch. 6 – Inductance and Capacitance
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Example:
Q2. The voltage across the terminals of a 5μF capacitor is
60
v   1500t
 A2te1500t
 A1e
The initial current in the capacitor is 100mA.
(a) Evaluate the coefficient A1 and A2.
(b) What is the expression for the capacitor current?
Part a)
Part b)
ELEC 250 – Summer 2015
t0
t 0
Ch. 6 – Inductance and Capacitance
Inductances in series
Leq  L1  L2  ...  Ln
i(t0 )  i1 (t0 )  i2 (t0 )  ...  in (t0 )
Inductances in parallel
1
1 1
1
   ... 
Leq L1 L2
Ln
i(t0 )  i1 (t0 )  i2 (t0 )  ...  in (t0 )
ELEC 250 – Summer 2015
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Ch. 6 – Inductance and Capacitance
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Example: Assume that the initial energy stored in the inductors of Fig. 1 is zero.
Find the equivalent inductance with respect to terminals a,b?
Solution:
(Fig. 1)
Note that the total initial current value is equal to zero.
ELEC 250 – Summer 2015
Ch. 6 – Inductance and Capacitance
Capacitors in series
1
1
1
1
 
 ... 
Ceq C1 C2
Cn
v(t0 )  v1 (t0 )  v2 (t0 )  ...  vn (t0 )
Capacitors in parallel
Ceq  C1  C2  ...  Cn
v(t0 )  v1 (t0 )  v2 (t0 )  ...  vn (t0 )
ELEC 250 – Summer 2015
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Ch. 6 – Inductance and Capacitance
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Example: Find the equivalent capacitance with respect to the terminals a, b for the
circuits shown in Fig. 2?
Solution:
(Fig. 2)
ELEC 250 – Summer 2015
Ch. 6 – Inductance and Capacitance
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Assignment 1: Assume that the initial energy stored
in the inductors of Figs. 1. is zero.
Find the equivalent inductance with
respect to terminals a,b?
Solution 1:
(Fig. 1)
Assignment 2: Find the equivalent capacitance with
respect to the terminals a,b for the
circuits shown in Fig. 2 ?
Solution 2:
(Fig. 2)
ELEC 250 – Summer 2015