Find it and nut for t 0 in the circuit of Fig 63 SolutionAt

Find i(t) and nu(t) for t > 0 in the circuit of Fig. 6^3

At t<0

I(0) = 0 A

V(t) = 40V

At t=0 current source activated

At t > 0 I.e, t= oo (infinity)

I(oo)= 0 A

V(oo) = ?

Equivalent resistance = 1+2+5 = 8 ohm.

Apply KVL to voltage source loop

-40-5(6)+v(oo) = 0

V(oo) = 70 V.

Time constant = LR/C

= 5*8/0.2= 200 sec

There fore

I(t)= I(oo)+{I(oo)-I(0)}exp(-t/T)

= 0 A

V(t) = v(oo)+{v(0)-v(oo)}exp(-t/T)

= 70+(40-70exp(-t/200)

= 70-30exp(-0.005t). V