Question

3. [15p] Assume that the switch in the circuit shown below has been in the position a for a long enough time, and then thrown to the position b, at t=0. R=0b R2-4k92 (a) [lp] Fort > 0, find the initial capacitor voltage at t = 0+sec, v.(0+). + OR + Vio V=100 ( voc=luf Ç v=51 I (b) [2p] For t > 0, find the final capacitor voltage at t → o sec, v..). (c) [3p] Find the numerical expression for vo(t), for t > 0. (a) [3p] Find the numerical expression for the capacitor current, i(t), for t > 0. (b) [6p] Draw qualitatively the found v.(t) and it), for t > 0. (Specify the initial and final values, and the time constant on the graphs.)

The R1 value is 2k

Answer 1

2k2 4kor M tso D 54 lo IMF- @ V, Cot) :- switch is placed position "a for a long at time » capacitor is open ciocuited 4ka vocot) (+) 57 Vocot) = 5v Voc): - capacitor switch is at aka is opened position "s" lov Voco) = lov Here Y= RC = 8x18x lxioo [p = 2x003

Now © Now Voct) = vca) + [voroty-ycode = 10+ [ 5-1032 +/Pixio [set) = 1o-se soot / fortzo zo * Here Here .()= c d Volt) d+ 6 = I x 1 [lo-se sot] = IKO [- se 5t-50) Test) = 2.5 € 5oot ma Time constant ?= axio's ภา= 2 mS cí vo (O) = -50010). 10- 50 luco) = 5v vo(a)= 10-50 500 (20) [vo cao) = nov

Volt) ist <volts) THE * € 4 6 8 10 -...og K 57 +(ms) 5x2ms =coms -500co) mA me ioco) = 2.50 Tioco) = 2.5mA i.co) = 2.52500ccm MA hym - 1 2 4 6 8 10 narod +(ms)