Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
ECA1212 Introduction to Electrical & Electronics Engineering Chapter 3: Capacitors and Inductors by Muhazam Mustapha, October 2011 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 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: LEQ = L1 + L2 + L3 L1 L2 L3 • Parallel combination: L1 L2 L3 CO2 1 1 1 1 L EQ L1 L 2 L3 Inductors Combination • Series: – Current is the same for all inductors – Equivalent flux is simple summation I1 I2 I3 Φ1 Φ2 Φ3 IEQ = I1 = I2 = I3 ΦEQ = Φ1 + Φ2 + Φ3 • Parallel: – Equivalent current is simple summation – flux is the same for all inductors Φ1 I1 Φ2 I2 Φ3 I3 IEQ = I1 + I2 + I3 CO2 ΦEQ = Φ1 = Φ2 = Φ3 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: C1 C2 C3 • Parallel combination: 1 1 1 1 CEQ C1 C1 C2 C3 CO2 CEQ = C1 + C2 + C3 C2 C3 Capacitors Combination • Series: – Charge is the same for all capacitors – Equivalent voltage is simple summation • Parallel: – Equivalent charge is simple summation – Voltage is the same for all capacitors Q1 Q2 Q3 V1 V2 V3 QEQ = Q1 = Q2 = Q3 VEQ = V1 + V2 + V3 Q1 V1 Q2 V2 Q3 V3 QEQ = Q1 + Q2 + Q3 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 dq dv i C dt dt 2 q 1Q 1 1 2 W Vdq dq CV VQ q 0 q 0 C 2 C 2 2 Q CO2 Q Capacitors • Charging Current: i V R V t / RC i e R i C V τ CO2 R time constant, τ = RC 2τ 3τ 4τ Charging period finishes after 5τ 5τ t Capacitors • Charging Voltage: v R C V v V v V (1 et / RC ) τ CO2 time constant, τ = RC 2τ 3τ 4τ Charging period finishes after 5τ 5τ t Capacitors • Discharging Current: R i C V i Discharging period finishes after 5τ τ 2τ V i e t / RC R V R CO2 3τ 4τ 5τ time constant, τ = RC t Capacitors • Discharging Voltage: v R C V v V v Ve t / RC τ CO2 time constant, τ = RC 2τ 3τ 4τ Discharging period finishes after 5τ 5τ t 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 d di v L dt dt 1 1 2 1 W Id d LI I 0 0 L 2 L 2 2 CO2 2 Inductors • Storing Current: i V R i V (1 e t /( L / R ) ) R i L V τ CO2 R time constant, τ = L/R 2τ 3τ 4τ Storing period finishes after 5τ 5τ t Inductors • Storing Voltage: v R L V v V v Vet /( L / R ) τ CO2 time constant, τ = L/R 2τ 3τ 4τ Storing period finishes after 5τ 5τ t Inductors • Decaying Current: i i τ V t /( L / R ) e R i L V V R CO2 R time constant, τ = L/R 2τ 3τ 4τ Decaying period finishes after 5τ 5τ t Inductors • Decaying Voltage: R L V v i Discharging period finishes after 5τ τ 2τ v Ve −V CO2 t /( L / R ) 3τ 4τ 5τ time constant, τ = L/R t