2. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 2
Capacitor
A capacitor is an electric device that can store energy in
the electric field between a pair of closely spaced
conductors
Passive circuit element which holds electric charge
Capacitor (C): Property which opposes the rate of
change of voltage;
The capacitive current is proportional to the rate of change of
voltage across it ;
ic = C (dv/dt)
Unit – Farad (F).
Circuit representation is
3. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 3
Capacitor…
The charge accumulated in a capacitor is proportional to the
potential difference across it.
This proportionality constant is the Capacitance.
Q = C V c
C
+
Vc
4. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 4
Equivalent Capacitance
In series
Q = C1V1 = C2V2 = … = CnVn
= CeqV
In parallel
Q1 = C1V; Q2 = C2V;
Qn = CnV
5. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 5
Capacitor Voltage and Charging Current
Charging of Capacitor through a Resistor
VV
RC
V
V
RC
1
:PI
:
RC
V
V
RC
1
dt
dV
0
dt
dV
C
R
VV
KCLApplying
PIC
PIC
1
C
C
CC
=
=
=
=+
=+
−
−
−
−
−
t
RC
CFC AeVCF
6. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 6
Capacitor Voltage and Charging Current
−=
+−=∴
−=∴+=
==
+=∴
−
−
−
t
RC
1
C
t
RC
1
C
C
t
RC
1
C
e1VV
VVeV
VAV;A0
0V0;At t
VAeV
7. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 7
Charging of a Capacitor
Time Constant, τ = RC
Time taken by the voltage of the capacitor to reach its final steady
state value, had the initial rate of rise been maintained constant
ic
vc
8. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 8
Discharging of Capacitor through a Resistor
Capacitor is initially charged to V volts
At t=0, switch is moved from position a to b
+
C v c
R
V
t = 0
a
b
i
9. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 9
Discharging of Capacitor through a Resistor
10. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 10
Energy stored in a Capacitor
2
0
Instantaneous power,
Energysupplied during is
Energystored when potentialdifference
increased from to volt is
J
0 V
1
2
oules
c
c c
c c
V
c c
dv
p v i C v
dt
dt
dw C v dv
W C v dv CV
= =
=
= =∫
11. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 11
Exercise
A Capacitor consists of 2 metal plates each 400 by 400 mm spaced 6
mm apart. The space between the metal plate is filled with a glass
plate 5 mm thick and a layer of paper 1 mm thick. The relative
permittivity of glass and paper are 8 and 2 respectively. Calculate the
equivalent capacitance. Also find the electric field strength in each
dielectric due to a potential difference of 10 kV between the metal
plate.
Ans:
Cg = 2.265 x 10-9
F; Cp = 2.832 x 10-9
F; Ceq = 1.258 x 10-9
F
Q = 1.258 x 10-5
C
Vg = 5.554 kV; Vp = 4.446 kV
Eg = 1.11 kV / mm ; Ep = 4.446 kV / mm
12. ELE 101 / 102 Dept of E & E Engg, MIT Manipal 12
A 10µF capacitor is initially charged to 100 V dc. It is then
discharged through a resistance R Ω and the p.d. across
the capacitor after 20 seconds is 50 V. Calculate the
value of R
Ans: 2.886MΩ
Exercise
