Question number 6 and 7. Question 7 follows up number 6. Thank you. the switch i

Question

Question number 6 and 7. Question 7 follows up number 6. Thank you.

the switch is changed? Bearing in mind that the current through the inductor cannot change instantly, find the voltage (passive sign notation) across the inductor just after the switch is changed. Determine the time constant, Tc, for the circuit for t > 0, determine the inductor current as time goes to infinity, and determine the inductor current at t = Tc. Both switches close at t = 0. Prior to t = 0 the switches had been open for a long time and the circuit was in steady state. Draw the circuit on your solutions and proceed. Find the time constant to for t>0. Find an expression for vc(t) for t > 0 and determine the value of vc at t = Tc. Continuing with question 5 find the power absorbed by resistor R2 at t = to

Explanation / Answer

Ceq = equivalent capacitance = C1+C2 = 8F

calculate the thevenin equivalent acorss capacitor:::

Rth= equivalent resistance across capacitor = (5|| (4+4)||6 = 2.033

let i = current through 5 ohm ::

apply KVL:: 20 -i(5+4) -(i+4)*(3||6) =0

20 -i(5+4) -(i+4)*(2) =0

20 -9i - 8-2i =0

i = 12/11

Vth = 20 -5*i = 20 -5*12/11 = 14.54 v

a) Time consatnt Tc = Rth*Ceq = 8*2.03 =16.27 s

b) Vc(t) = Vth[1-e^(-t/Tc)]

= 14.54[1-e^(-t/16.27)]

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