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Unformatted text preview: 1 ECE201 Linear Circuit Analysis I Lecture 16. Topic: Capacitor and Capacitance 1. What is a capacitor? Usually made of two metal plates separated by air or other insulating material. Capacitors tend to resist sudden changes in voltage across the plates. 2. Capacitance (2) unit of C: farads (F) (3) i-v relationship i c (t) = C dv c (t) dt (compare with v L (t) = L di L (t) dt ) thus 1 F = 1 A-sec/v (4) v-i relationship v c (t) = 1 C −∞ t ∫ i c ( τ )d τ Equivalently, d τ ) τ ( i C 1 d τ ) τ ( i 1 ) t ( v t t C t- C C ∫ + ∫ = ∞ C v L (t o ) = Initial condition Like the inductor, a capacitor has memory. v c (t) = v c (t o ) + 1 C t o t ∫ i c ( τ )d τ v c (t) i c (t) → + – C (1) Symbol: C (passive-sign convention) 2 3. Continuity Property of Capacitor (Voltage) (1) If i c (t) is bounded, then v c (t) is continuous: v c (t − ) = v c (t + ). (2) unit step function and impulse function step function: u(t) = 1 t ≥ 0.w....
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This note was uploaded on 04/19/2011 for the course ECE 201 taught by Professor All during the Spring '08 term at Purdue.
- Spring '08