Question

Given: 1. Exact arithmetic will yield a pair of purely imaginary poles plus a real pole. 2. i,(t) Iu(t) Amps Do: a) Find and draw a Laplace Transformed Network (LTN) b) Find the Laplace transform of the output quantity, I(s). Express your answer in the following form: bs2bis+bo H(s) 3as2 + a18+ a Amp seconds i. Find the coefficients of the partial fraction expansion (PFE) using the Heaviside covering method. c) ii. Find the time-domain i(t) (in units of Amps) by inspection of the PFE Express terms of is(t) in the final answer of c)ii. as an exponential function plus a single cosine with a phase angle in the following format: .. KRe Ko cos (wt + 0)... where a is in sec, w, is in rad/sec, and 0 is in degrees. Indicate the units for the angle in your final answer by including a superscript. For example, if the answer is a current where: KR 871.96 uAmps, Kc = 4.1104 mA a 0.63 x 10 sec, wo7.5304 krad/sec, and 0-74.9 degrees, write the angle unit as a superscript, e.g. -74.9. Then the complete answer for part c) looks like 63 x 10t + 4.11 x 103 cos ((7.53 x 10)t-74.9°) Amps 1t)= 872 x 10-e Some of the constants in the answers to any of the parts might be zero. Be sure to double underline the final answers and include units for all parts, viz. a), b), c)i., and c)ii. The units of the PFE coefficients in part c) i. are Amps There must be no complex numbers in your final answers. saaar R1 25 kOhms L1 1 mH L2 2 uH C = 2 nF Ix 4 A Ai = 500 A/A

Answer 1

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Apply Nd abe Va - A, 6)R a S and Sulostitute s) in oq O git Va -A, (, Va S + L S C C 4 S (s

-T A R4) s+ (EnuR,) RiCSt AT (Ix- L2c+R+40+AR CL