ECA1212 Introduction to Electrical & Electronics Engineering Chapter 3: Capacitors and Inductors by...
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Transcript of ECA1212 Introduction to Electrical & Electronics Engineering Chapter 3: Capacitors and Inductors by...
ECA1212Introduction to Electrical &
Electronics EngineeringChapter 3: Capacitors and Inductors
by Muhazam Mustapha, October 2011
Learning Outcome
• Understand the formula involving capacitors and inductors and their duality
• Be able to conceptually draw the I-V characteristics for capacitors and inductors
By the end of this chapter students are expected to:
Chapter Content
• Units and Measures
• Combination Formula
• I-V Characteristics
Units and Measures
CO2
Capacitors
• Capacitors are electric devices that store static electric charge on two conducting plates when voltage is applied between them.
• Energy is stored as static electric field between the plates.
+++++++++++++++++++++++++++
−−−−−−−−−−−−−−−−−−−−−−−−−−−
Electrostatic Field
CO2
Capacitance, Charge & Voltage
• Capacitance: The value of a capacitor that maintains 1 Coulomb charge when applied a potential difference of 1 Volt across its terminals.
Q = CV
Q = charge, C = capacitance (farad),V = voltage
CO2
Inductors
• Inductors are electric devices that hold magnetic field within their coils when current is flowing through them.
• Energy is stored as the magnetic flux around the coils.
Magnetic Field
CO2
Inductance, Magnetic Flux & Current• Inductance: The value of an inductor that
maintains 1 Weber of magnetic flux when applied a current of 1 Ampere through its terminals.
Φ = LI
Φ = magnetic flux, L = inductance (henry),I = current
CO2
Combination Formula– Duality Approach
CO2
Inductors Combination
• Inductors behave (or look) more like resistors.• Hence, circuit combination involving inductors
follow those of resistors.• Series combination:
L1 L2 L3
LEQ = L1 + L2 + L3
• Parallel combination:L1
L2
L3321EQ L
1
L
1
L
1
L
1
CO2
Inductors Combination
I1 I2 I3
IEQ = I1 = I2 = I3
Φ1
Φ2
Φ3
• Series:– Current is the same for all
inductors– Equivalent flux is simple
summation
• Parallel:– Equivalent current is simple
summation– flux is the same for all inductors
Φ1 Φ2 Φ3
ΦEQ = Φ1 + Φ2 + Φ3
I1
I2
I3
ΦEQ = Φ1 = Φ2 = Φ3
IEQ = I1 + I2 + I3
CO2
Capacitors Combination• The inverse of resistors are conductors; and the
dual of inductors are capacitors.• If inductors behave like resistors, then
capacitors might behave like conductors – in fact they are.
• Series combination:• Parallel combination:
C1 C2 C3
CEQ = C1 + C2 + C3
C1
C2
C3
321EQ C
1
C
1
C
1
C
1
CO2
Capacitors Combination• Series:
– Charge is the same for all capacitors
– Equivalent voltage is simple summation
Q1 Q2 Q3
QEQ = Q1 + Q2 + Q3
Q1
Q2
Q3
QEQ = Q1 = Q2 = Q3
V1 V2 V3
• Parallel:– Equivalent charge is simple
summation– Voltage is the same for all
capacitors
V1
V2
V3
VEQ = V1 = V2 = V3
VEQ = V1 + V2 + V3
CO2
I-V Characteristics
CO2
Capacitors
• At the instant of switching on, capacitors behave like a short circuit.
• Then charging (or discharging) process starts and stops after the maximum charging (discharging) is achieved.
• When maximum charging (or discharging) is achieved, i.e. steady state, capacitors behave like an open circuit.
• Voltage CANNOT change instantaneously, but current CAN.
CO2
Capacitors
• I-V relationship and power formula of a capacitor
dt
dvC
dt
dqi
VQCVC
Qdq
C
qVdqW
Q
q
Q
q 2
1
2
1
2
1 22
00
CO2
Capacitors• Charging Current:
i
t
RCteR
Vi /
V
R
C
i
time constant, τ = RC
τ 2τ 4τ3τ 5τ
R
V
Charging period finishes after 5τ
CO2
Capacitors• Charging Voltage:
v
t
)1( / RCteVv
V
R
C v
time constant, τ = RC
τ 2τ 4τ3τ 5τ
Charging period finishes after 5τ
V
CO2
Capacitors• Discharging Current:
i
t
RCteR
Vi /
V
R
C
i
time constant, τ = RC
τ 2τ 4τ3τ 5τ
R
V
Discharging period finishes after 5τ
CO2
Capacitors• Discharging Voltage:
v
t
RCtVev /
V
R
C
time constant, τ = RC
τ 2τ 4τ3τ 5τ
Discharging period finishes after 5τ
V
v
CO2
Inductors
• At the instant of switching on, inductors behave like an open circuit.
• Then storage (or decaying) process starts and stops after the maximum (minimum) flux is achieved.
• When maximum (or minimum) flux is achieved, inductors behave like a short circuit.
• Current CANNOT change instantaneously, but voltage CAN.
CO2
Inductors
• I-V relationship and power formula of a inductor
dt
diL
dt
dv
ILIL
dL
IdW
2
1
2
1
2
1 22
00
CO2
Inductors• Storing Current:
i
t
)1( )//( RLteR
Vi
V
R
L
time constant, τ = L/R
τ 2τ 4τ3τ 5τ
Storing period finishes after 5τ
i
R
V
CO2
Inductors• Storing Voltage:
v
t
)//( RLtVev time constant, τ = L/R
τ 2τ 4τ3τ 5τ
Storing period finishes after 5τ
V
V
R
L v
CO2
Inductors• Decaying Current:
i
t
)//( RLteR
Vi time constant, τ = L/R
τ 2τ 4τ3τ 5τ
Decaying period finishes after 5τ
V
R
L
i
R
V
CO2
Inductors• Decaying Voltage:
i
t
)//( RLtVev time constant, τ = L/R
τ 2τ 4τ3τ 5τ
Discharging period finishes after 5τ
−V
V
R
L v
CO2