In the following circuit: If vs (t) is given as a square waves as shown: If L=2H and R=492, Find i(t)? Vs (t)⭑ 8 Solution: Vs (t) 3 5 i(t) R Example 1: In the following circuit: If v,(t) is given as a square waves, If L=2H and R=492, Find i(t)? Vs (1)4 10 -π/2 π/2 3/2 2π 5/2 t t=0 i(t) R Vs (t) + Solution: Since T= then 10 = 2π/T = 2 rad/s 2/דר 30= dt = = 10 at 10 dt = 5 an an πο f(t) cos(noot)dt /2 10 cos(2nt)dt = 0 元 T f(t) sin(noot)dt bn = /2 20 bn 10 sin(2nt)dt for odd n пл So, Fourier Transformation of V, (t): 00 20 Vs (t)=5+Σ sin(2nt) ηπ odd n Now, we need to find i(t) for: 1- V, (t) = 5V using Laplace Analysis: V(s) 5/s 5 5/2 11(s)- = Z(s) (SL+R) s(2s+4) s(s+2) 5/4 5/4 = 11(s) S (s+2) 11(t)=(5/4) -(5/4) e 2-Vs (t)=- 20 -21 sin(2nt) using frequency analysis: nπ 20 V= ηπ & 0-2n Z=R+joL=4+ j(2n)(2) = 4+ j4n=4(1+jn) V 5 5 I= = /-tan 'n Z nл(1+jn) n√√1+n² 5 i2(t) sin(2nt-tan h) n√1+n² The complete solution is: 00 i(t) = i(t) + Σ i2(t) odd n

In the following circuit: If vs (t) is given as a square waves as shown: If L=2H and R=492, Find i(t)? Vs (t)⭑ 8 Solution: Vs (t) 3 5 i(t) R Example 1: In the following circuit: If v,(t) is given as a square waves, If L=2H and R=492, Find i(t)? Vs (1)4 10 -π/2 π/2 3/2 2π 5/2 t t=0 i(t) R Vs (t) + Solution: Since T= then 10 = 2π/T = 2 rad/s 2/דר 30= dt = = 10 at 10 dt = 5 an an πο f(t) cos(noot)dt /2 10 cos(2nt)dt = 0 元 T f(t) sin(noot)dt bn = /2 20 bn 10 sin(2nt)dt for odd n пл So, Fourier Transformation of V, (t): 00 20 Vs (t)=5+Σ sin(2nt) ηπ odd n Now, we need to find i(t) for: 1- V, (t) = 5V using Laplace Analysis: V(s) 5/s 5 5/2 11(s)- = Z(s) (SL+R) s(2s+4) s(s+2) 5/4 5/4 = 11(s) S (s+2) 11(t)=(5/4) -(5/4) e 2-Vs (t)=- 20 -21 sin(2nt) using frequency analysis: nπ 20 V= ηπ & 0-2n Z=R+joL=4+ j(2n)(2) = 4+ j4n=4(1+jn) V 5 5 I= = /-tan 'n Z nл(1+jn) n√√1+n² 5 i2(t) sin(2nt-tan h) n√1+n² The complete solution is: 00 i(t) = i(t) + Σ i2(t) odd n

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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