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ask z Show that the LRC circuit given below can be described by the differential equation L d²i + R di + 1 = 0 dt² dt C If L = 0.192 Henry; C = 30 x 106 farads and R = 160 ohms, solve the equation given that when time t= 0. i = 0 and di = 50 dt E C

ask z Show that the LRC circuit given below can be described by the differential equation L d²i + R di + 1 = 0 dt² dt C If L = 0.192 Henry; C = 30 x 106 farads and R = 160 ohms, solve the equation given that when time t= 0. i = 0 and di = 50 dt E C

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Task 2 Show that the LRC circuit given below can be described by the differential equation L d²i + R di + 1 = 0 dt² dt C If L = 0.192 Henry; C = 30 x 10-6 farads and R = 160 ohms, solve the equation given that when time t = 0. i = 0 and di = 50 dt E R C
Transcribed Image Text:Task 2 Show that the LRC circuit given below can be described by the differential equation L d²i + R di + 1 = 0 dt² dt C If L = 0.192 Henry; C = 30 x 10-6 farads and R = 160 ohms, solve the equation given that when time t = 0. i = 0 and di = 50 dt E R C
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It makes sense up to that point but I'm getting a little confused on how you got C1 & C2.

Solution of differential equation will i(t) = C₁e At t = 0, i(0) = C₁e 0 = C₁+C₂ i(t) dt 50 1250 3 = Solve both equation, we get Differentiate i(t) w. r. t time, we get 1250, -t C₂e-t 1250 3 1250 3 C₁ C₂ -XO 1250 3 -t = = + C₂e-t + C₂e-⁰ (1) C₁e 3 C₁ - C₂ 150 1247 150 1247 - (2)
Transcribed Image Text:Solution of differential equation will i(t) = C₁e At t = 0, i(0) = C₁e 0 = C₁+C₂ i(t) dt 50 1250 3 = Solve both equation, we get Differentiate i(t) w. r. t time, we get 1250, -t C₂e-t 1250 3 1250 3 C₁ C₂ -XO 1250 3 -t = = + C₂e-t + C₂e-⁰ (1) C₁e 3 C₁ - C₂ 150 1247 150 1247 - (2)
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