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ee250_HW3_sol

# ee250_HW3_sol - EE 250 Winter 2010 University of Alberta...

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EE 250 Winter 2010 University of Alberta HOMEWORK 3 (due Monday Jan 25 th , 2010) Instructor : Karthik Shankar (Make sure your answers show the work in solving the problem. If the final answer is wrong, partial credit will be provided if the work is shown to have made progress towards the solution. Do not expect any credit if the T.A. cannot logically follow what you have put on your submitted homework) 1. Find 0 ( ) for 0. i t t SOLUTION 1

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2. Design a parallel RLC circuit with R = 1 kΩ which has the following characteristic equation : SOLUTION 2
3. Find ( ) for 0 in the circuit below. c v t t 2 2 2 0 0 1 2 2 0 2 2 2 1 0 1 1 2 0 is the characteristic equation where 25 1 0.04 1 1 For a parallel RLC ckt, = 1.5625 rad s ; Since , the ckt is underdamped. 2 2 8 0.04 25 1.5625 4.75 rad s ( ) d c s s LC RC v t α ϖ - - + + = = = = × = = < × × = - = - = 1 2 3 1 2 3 ( cos sin ) (1) At , the inductor is fully charged and shorts the capacitor 0 (2) Since (0 ) (0 ) 8, 8. At this point, only is lef t d d c c K e K t K t t K v v K K - - + = + + = ∞ = = = = 0 0 2 3 0 3 t to be found. (0) (0 ) (0 ) 0 25 (3) After differentiating eqn (1) and setting 0, we obtain 1.5625 4.75 (4) From eqns (2), (3) and (4), =-2.6 c c c L L t t c t v dv dv i i C R dt dt dv t K K dt K - + = = = = = = + = - = = - + { } 1.5625 3 ( ) 8cos(4.75 ) 2.63sin(4.75 ) V t c v t e t t - = - 3

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Find ( ) for 0 in the circuit below o v t t and plot the response including the time interval just prior to closing the switch. SOLUTION
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ee250_HW3_sol - EE 250 Winter 2010 University of Alberta...

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