ECA1212 Introduction to Electrical & Electronics Engineering Chapter 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: L1L1 L2L2 L3L3 L EQ = L 1 + L 2 + L 3 Parallel combination: L1L1 L2L2 L3L3 CO2

Inductors Combination I1I1 I2I2 I3I3 I EQ = I 1 = I 2 = I 3 Φ1Φ1 Φ2Φ2 Φ3Φ3 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 Φ1Φ1 Φ2Φ2 Φ3Φ3 Φ EQ = Φ 1 + Φ 2 + Φ 3 I1I1 I2I2 I3I3 Φ EQ = Φ 1 = Φ 2 = Φ 3 I EQ = I 1 + I 2 + I 3 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: C1C1 C2C2 C3C3 C EQ = C 1 + C 2 + C 3 C1C1 C2C2 C3C3 CO2

Capacitors Combination Series: –Charge is the same for all capacitors –Equivalent voltage is simple summation Q1Q1 Q2Q2 Q3Q3 Q EQ = Q 1 + Q 2 + Q 3 Q1Q1 Q2Q2 Q3Q3 Q EQ = Q 1 = Q 2 = Q 3 V1V1 V2V2 V3V3 Parallel: –Equivalent charge is simple summation –Voltage is the same for all capacitors V1V1 V2V2 V3V3 V EQ = V 1 = V 2 = V 3 V EQ = V 1 + V 2 + V 3 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 CO2

Capacitors Charging Current: i t V R C i time constant, τ = RC τ2τ2τ4τ4τ3τ3τ5τ5τ Charging period finishes after 5 τ CO2

Capacitors Charging Voltage: v t V R C v time constant, τ = RC τ2τ2τ4τ4τ3τ3τ5τ5τ Charging period finishes after 5 τ V CO2

Capacitors Discharging Current: i t V R C i time constant, τ = RC τ2τ2τ4τ4τ3τ3τ5τ5τ Discharging period finishes after 5 τ CO2

Capacitors Discharging Voltage: v t V R C time constant, τ = RC τ2τ2τ4τ4τ3τ3τ5τ5τ Discharging period finishes after 5 τ 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 CO2

Inductors Storing Current: i t V R L time constant, τ = L/R τ2τ2τ4τ4τ3τ3τ5τ5τ Storing period finishes after 5 τ i CO2

Inductors Storing Voltage: v t time constant, τ = L/R τ2τ2τ4τ4τ3τ3τ5τ5τ Storing period finishes after 5 τ V V R L v CO2

Inductors Decaying Current: i t time constant, τ = L/R τ2τ2τ4τ4τ3τ3τ5τ5τ Decaying period finishes after 5 τ V R L i CO2

Inductors Decaying Voltage: i t time constant, τ = L/R τ2τ2τ4τ4τ3τ3τ5τ5τ Discharging period finishes after 5 τ −V−V V R L v CO2