Lecture 10 Capacitor and Inductor Hung-yi Lee

Outline Capacitor (Chapter 5.1) Inductor (Chapter 5.2) Comparison of Capacitor and Inductor Superposition for Dynamic Circuits

Outline Capacitor (Chapter 5.1) Inductor (Chapter 5.2) Comparison of Capacitor and Inductor Superposition for Dynamic Circuits

Capacitor – i-v characteristics If v is constant i=0 Open circuit Dynamic reference current should flow from “+” to “-”

Capacitor – i-v characteristics

Continuity - Capacitor The voltage of capacitor should be continuous Infinite current Current changes

Capacitor – Power and Energy Instantaneous consumed power of a capacitor: Total energy consumed: Depend on voltage at t The energy stored

Capacitor - Application Automated external defibrillators (AED)

Capacitor - Application Automated external defibrillators (AED) 5000V

Capacitor - Series

Capacitor - Parallel C par =C 1 +C 2 + ‥ ‥ ‥ +C N

Outline Capacitor (Chapter 5.1) Inductor (Chapter 5.2) Comparison of Capacitor and Inductor Superposition for Dynamic Circuits

Inductor – i-v characteristics If i=constant v=0 short circuit Dynamic reference current should flow from “+” to “-”

Inductor – i-v characteristics

Continuity - Inductor The current of inductor should be continuous Infinite Voltage Voltage changes

Shock by Inductor

Inductor – Power and Stored Energy Instantaneous consumed power of an inductor Total Energy consumed Depend on current at t The energy stored

Inductor - Series L ser =L 1 +L 2 + ‥ ‥ ‥ +L N

Inductor - Parallel

Outline Capacitor (Chapter 5.1) Inductor (Chapter 5.2) Comparison of Capacitor and Inductor Superposition for Dynamic Circuits

Summary - i-v characteristics 愛愛 CVV L

Summary - Series and Parallel Series Parallel i-v Resistor Capacitor Inductor

Outline Capacitor (Chapter 5.1) Inductor (Chapter 5.2) Comparison of Capacitor and Inductor Superposition for Dynamic Circuits

Review This equation only for circuits with sources and resistors. y: any current or voltage for an element x i : current of current sources or voltage of voltage sources Proportionality Principle, Superposition Principle Can be used in any circuit in this course

Linearity A circuit is a multiple-input multiple-output (MIMO) system Input: current of current sources or voltage of voltage sources Output: the current or voltage for the elements + - Circuit (System) input output

Linearity All linear circuits are linear system Linear Circuit: Sources Linear Elements: Resistor, Capacitor, Inductor All circuits in this course are linear circuits.

Linearity Linear System: Property 1: Input: g 1 (t), g 2 (t), g 3 (t), …… output: h 1 (t), h 2 (t), h 3 (t), …… Input: Kg 1 (t), Kg 2 (t), Kg 3 (t), …… output: Kh 1 (t), Kh 2 (t), Kh 3 (t), …… Proportionality Principle

Linearity Linear System: Property 2: Input: a 1 (t), a 2 (t), a 3 (t), …… output: x 1 (t), x 2 (t), x 3 (t), …… Input: a 1 (t)+ b 1 (t), a 2 (t)+ b 2 (t), a 3 (t)+ b 3 (t), …… output: x 1 (t)+y 1 (t), x 2 (t)+y 2 (t), x 3 (t)+y 3 (t), …… Superposition Principle Input: b 1 (t), b 2 (t), b 3 (t), …… output: y 1 (t), y 2 (t), y 3 (t), ……

Linearity Linear System: Property 2: Input: a 1 (t), a 2 (t), a 3 (t), …… output: x 1 (t), x 2 (t), x 3 (t), …… Input: a 1 (t)+ b 1 (t), a 2 (t)+ b 2 (t), a 3 (t)+ b 3 (t), …… output: x 1 (t)+y 1 (t), x 2 (t)+y 2 (t), x 3 (t)+y 3 (t), …… Superposition Principle Input: b 1 (t), b 2 (t), b 3 (t), …… output: y 1 (t), y 2 (t), y 3 (t), ……

Linearity Superposition Principle can be applied on all circuits in this course (Textbook: Chapter 6.5).

Announcement 10/22 ( 三 ) 第一次小考 Ch1. Circuit Variables and Laws (1.4, 1.5) Ch2. Properties of Resistive Circuits (2.3, 2.4, 2.5) Ch3. Applications of Resistive Circuits (3.2) Ch4. Systematic Analysis Methods (4.1, 4.2, 4.3, 4.4) 助教時間：週一到週四 PM6:30~8:30 助教 : 黃盈庭 時間 : 週三 PM6:30~8:30 地點 : 電二 146

Thank you!

Appendix

Capacitor – Series (2) If v is constant i=0 Open circuit What are v 1, v 2 ……?

Capacitor Application How Capacitive Liquid Level Sensors Work

Acknowledgement 感謝 林楷恩 (b02) 指出投影片中 Equation 的錯誤