This document discusses inductance and capacitance. It defines an inductor as a coil of conducting wire that exhibits opposition to changes in current flowing through it. A capacitor consists of two conducting plates separated by an insulator. The document describes the relationships between voltage, current, power, and energy for inductors and capacitors. It also covers series and parallel combinations of inductors and capacitors and how their equivalent inductance/capacitance is calculated.

1. Inductance and Capacitance
Susmitha roy vatturi

2. Inductance and
Capacitance
• Inductor
• Relationship between voltage,
current, power and energy
• Capacitor
• Relationship between voltage,
current, power and energy
• Series-parallel combinations for
inductance and capacitance

3. Inductor

4. Inductor concept
• An inductor consist of a coil of conducting
wire.
• Inductance, L is the property whereby an
inductor exhibits opposition to the change
of current flowing through it, measured in
henrys (H).

5. Inductance
• Inductance, L

AN
L
µ2
=
L = inductance in henrys (H).
N = number of turns
µ = core permeability
A = cross-sectional area (m2)
ℓ = length (m)

6. Relationship between voltage,
current, power and energy
−+ )(tv
)(ti L
Inductor
symbol
dt
tdi
Ltv
)(
)( =
Inductor
Voltage

7. ∫ +=
t
t
tidv
L
ti
0
)()(
1
)( 0ττ
Inductor
current
( )



+=
==
∫
t
t
0
0
tidtv
L
1
v
dt
di
Livip
Power

8. • Assuming that energy is zero at time
t=t0, then inductor energy is:
)(
2
1)( 2
tLitw =
)(
2
1
)(
2
1
)()()(
0
22
0
0
tLitLi
dptwtw
t
t
−=
=− ∫ ττ

9. CAPACITOR

10. Capacitor physical
concept:
• A capacitor consists of two
conducting plates separated by an
insulator (or dielectric).
• Capacitance, C is the ratio of the
charge on one plate of a capacitor to
the voltage difference between the
two plates, measured in farads (F).

11. • The amount of charge stored,
represented by q, is directly proportional
to the applied voltage v,
q = cas dalam coulomb (C)
C = kapasitans dalam farad (F)
v = voltan dalam volt (V)
vCq =

12. • Capacitance, C:
d
eA
C =
C = Capacitance in farads (F)
e = permittivity of dielectric material
between the plates (C2/N∙m2)
A = surface area of each plates (m2)
d = distance between the plates (m)

13. −+ )(tv
)(ti C
R elationship between
voltage, current, power
and energy
• Capacitor symbol

14. dt
)t(dv
C)t(i =CapacitorCapacitor
currentcurrent
∫ +=
t
t
tvdi
C
tv
0
)()(
1
)( 0ττ
Capacitor voltageCapacitor voltage

15. Power:






×=
×=
dt
tdv
Ctv
titvtp
)(
)(
)()()(

16. • Energy stored in a capacitor from time t to t0:
2
0
2
)(
)(
2
)(
)(
0
)(
2
1
)(
2
1
)(
2
1
)()(
)(
)(
)()()(
0
0
0
0
tvCtvC
vC
dvvC
d
d
dv
Cv
dptwtw
tv
tv
tv
tv
t
t
t
t
−=
=
=
=
=−
∫
∫
∫
τ
ττ
τ
τ
τ
τ
ττ

17. • Capacitor is not discharge at t=-∞,
therefore the voltage is zero.
2
)(
2
1
)( tvCtw =
Energy capacitor

18. 1C 2C NC
1i 2i
Ni
−
+
v
Series and parallel
capacitors
• The equivalent capacitance, Ceq of N
parallel-connected capacitors is the sum
of the individual capacitances.

19. • Using KCL,
NIIII +++= .........21
( )
dt
dv
C
dt
dv
C
dt
dv
CCC
dt
dv
C
dt
dv
C
dt
dv
CI
eq
N
n
n
N
N
=





=
+++=
+++=
∑=1
21
21
.......
...........
dt
dv
CI nn =

20. • Equivalent circuit for the parallel
capacitor,
∑=
=
N
n
neq CC
1
eqCsi
−
+
v

21. 1C
sV
−
+
2C
NC
−+ 1V −+ 2V
i
−
+
NV
• The equivalent capacitance, Ceq of N
series-connected capacitors is the
reciprocal of the sum of the reciprocals
of the individual capacitances.

22. • Using KCL,
NVVVV +++= ...........21
∫
∫∑
∫
∞−
∞−
=
∞−
=
=






+++=
t
eq
tN
n n
t
N
di
C
di
C
di
CCC
V
ττ
ττ
ττ
)(
1
)(
1
)(
1
........
11
1
21
∫ ∞−
=
t
n
n di
C
V ττ)(
1

23. ∑=
=
N
n neq CC 1
11
sV
−
+
eqC
i
• Equivalent circuit for the series
capacitor,

24. Series and parallel
inductors
sV
−
+
i
−+ 1V −+ 2V
−
+
NV
1L 2L
NL
• The equivalent inductance, Leq of N
series-connected inductors is the sum of
the individual inductances.

25. • Using KVL,
NVVVV +++= .........21
( )
dt
di
L
dt
di
L
dt
di
LLL
dt
di
L
dt
di
L
dt
di
VV
eq
N
n
n
N
N
=





=
+++=
+++=
∑=1
21
21
.......
...........
dt
di
LV nn =

26. ∑=
=
N
n
neq LL
1
sV
−
+
i
eqL
• Equivalent circuit for the series
inductor,

27. si 1L
−
+
V 2L NL
2i1i Ni
• The equivalent inductance, Leq of N
parallel-connected inductors is the
reciprocal of the sum of the reciprocals
of the individual capacitances.

28. • Using KVL,
NIIII +++= ...........21
∫
∫∑
∫
∞−
∞−
=
∞−
=
=






+++=
t
eq
tN
n n
t
N
dv
L
dv
L
dv
LLL
I
ττ
ττ
ττ
)(
1
)(
1
)(
1
........
11
1
21
∫ ∞−
=
t
n
n dv
L
I ττ)(
1

29. ∑=
=
N
n neq LL 1
11
si eqL
−
+
V
• Equivalent circuit for the parallel
inductor,

30. Capacitance :
• When voltage across a capacitor is
increased or decreased, the capacitor
"resists" the change
• The current alters the charge on a capacitor
• Capacitor is directly proportional to the
rate of change of the voltage across those
plates
• As the supply voltage increases and
decreases, the capacitor charges and
discharges

31. S.C & O.C
CHARACTERISTICS :
• At DC (zero frequency) an inductor
behaves like a short circuit and a
capacitor behaves like an open circuit
• capacitor function as an open circuit at
low frequencies, while at high frequencies
it acts as a short circuit?

32. Thank you …..