If K is opened at t=0, Find v, dv/dt and d2v/dt2 at t=0+, If I=1 amp, R=100 Ω , and
As per the steps indicated :
6. Previous history before the switch is opened indicates that the switch Is closed
iL(0-) =0 .
7. Write the general circuit after switching :
Inductor acts as open , as inductor will not allow current to change
Hencev(0+) =i*R=100 V
8. Write general network after switching :
I= v/r + 1/L ∫
9. Obtain an expression for the first derivative:
Diff we get dv/dt at to0+ = -10000V/sec
10. Obtain an expression for the second derivative:
d2v(0+)/dt2 = - R/L dv/dt , substituting the known values we get 10*106 V/s2 .
Ans: 100, -104 v/sec , 106 v/s2