Lesson 13

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Purdue University *

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20001

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Electrical Engineering

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Oct 30, 2023

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Lesson 13 (W, 9/20/2022): Capacitance and Capacitors ( con’t ); Inductance and Inductors Fall 2023 Prof: J. D. McKinney, mckinnjd@purdue.edu OH: TRF, 3 4 pm 1
1. Capacitance and capacitors. 2. Inductors and inductance. 3. C and L combinations. Outline
Capacitors: i-v characteristic 3 ? 𝑡 = ? ( 𝑡 0 ) + 1 ? ? 0 ? 𝑖 𝑡 𝑑 𝑡 𝑖 ( 𝑡 ) = ? 𝑑? ( 𝑡 ) 𝑑𝑡 ? = 2𝐹
Capacitors: DC & Steady State Behavior 4 A capacitor in steady-state or DC conditions behaves as an: 𝑖 ( 𝑡 ) = ? 𝑑? ( 𝑡 ) 𝑑𝑡 R 1 + V s R 2 - + v C - open circuit (with a voltage across it!)
Capacitors: Energy Storage 5 𝑝 𝑡 = ? 𝑡 𝑖 𝑡 = ? 𝑡 ? 𝑑? ( 𝑡 ) 𝑑𝑡 ? 𝑡 = ? 𝑡 0 + ? 0 ? 𝑝 𝑡 𝑑 𝑡 = ? 𝑡 0 + ? ? 0 ? ? ( 𝑡 ) 𝑑? ( 𝑡 ) 𝑑 𝑡 𝑑 𝑡 ? 𝑡 = 1 2 ? ? 2 ( 𝑡 ) ? 0 ? = 1 2 ? ? 2 𝑡 ? 2 ( 𝑡 0 ) ? 𝑡 = 1 2 ? ? 2 𝑡
Capacitors: Energy Storage Example 1 6 For the following circuit find: 1. The energy stored in the capacitor at 𝑡 = ∞ . 2. The stored energy change in the capacitor from 𝑡 = 0 to 𝑡 = ∞ . 1. Circuit at 𝑡 = ∞ . ? 𝑐 = 24 ? 10 Ω 10 Ω + 2 Ω = 20 ? ? 𝑐 = 1 2 ? ? 𝑐 2 = 1 2 100 ?𝐹 20 ? 2 = 20 ?
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