1. EEE1012 Introduction to Electrical & Electronics Engineering Chapter 3: Capacitors and Inductors by Muhazam Mustapha, August 2010

2. Learning Outcome By the end of this chapter students are expected to:
Understand the formula involving capacitors and inductors and their duality
Be able to conceptually draw the I-V characteristics for capacitors and inductors

3. Chapter Content Units and Measures Combination Formula
I-V Characteristics

4. Units and Measures

5. 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
−−−−−−−−−−−−−−−−−−−−−−−−−−−

6. 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

7. 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

8. 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

9. Combination Formula – Duality Approach

10. Inductors Combination
Inductors behave (or look) more like resistors.
Hence, circuit combination involving inductors follow those of resistors.
Series combination:
LT = L1 + L2 + L3 L1 L2 L3
Parallel combination: L1 L2 L3

11. Inductors Combination
Series:
Current is the same for all inductors
Total flux is simple summation I1 I2 I3 Φ1 Φ2 Φ3
IT = I1 = I2 = I3
ΦT = Φ1 + Φ2 + Φ3 Φ1 I1
Parallel:
Total current is simple summation
flux is the same for all inductors Φ2 I2 Φ3 I3
IT = I1 + I2 + I3
ΦT = Φ1 = Φ2 = Φ3

12. 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 C1 C2
CT = C1 + C2 + C3 C3

13. Capacitors Combination
Series:
Charge is the same for all capacitors
Total voltage is simple summation Q1 Q2 Q3 V1 V2 V3
QT = Q1 = Q2 = Q3
VT = V1 + V2 + V3
Parallel:
Total charge is simple summation
Voltage is the same for all capacitors Q1 V1 Q2 V2 Q3 V3
QT = Q1 + Q2 + Q3
VT = V1 = V2 = V3

14. I-V Characteristics

15. 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.

16. Capacitors
I-V relationship and power formula of a capacitor

17. Capacitors Charging Current: time constant, τ = RC R i i C V t τ 2τ 3τ4τ 5τ
Charging period finishes after 5τ

18. Capacitors Charging Voltage: time constant, τ = RC R v C v V V t τ 2τ3τ 4τ 5τ
Charging period finishes after 5τ

19. Capacitors Discharging Current: time constant, τ = RC R i C V i
Discharging period finishes after 5τ t τ 2τ 3τ 4τ 5τ
time constant, τ = RC

20. Capacitors Discharging Voltage: time constant, τ = RC R v C v V V t τ2τ 3τ 4τ 5τ
Discharging period finishes after 5τ

21. 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.

22. Inductors
I-V relationship and power formula of a inductor

23. Inductors Storing Current: time constant, τ = L/R R i i L V t τ 2τ 3τ4τ 5τ
Storing period finishes after 5τ

24. Inductors Storing Voltage: time constant, τ = L/R R v L v V V t τ 2τ3τ 4τ 5τ
Storing period finishes after 5τ

25. Inductors Decaying Current: time constant, τ = L/R R i i L V t τ 2τ 3τ4τ 5τ
Decaying period finishes after 5τ

26. Inductors Decaying Voltage: time constant, τ = L/R R L v V i
Discharging period finishes after 5τ t τ 2τ 3τ 4τ 5τ
time constant, τ = L/R −V