Solve Transient Analysis Problem: Find I0

[php]

i was trying to solve this question(file attached), but i can only come up with the answer:

i assumed i_L=0 at t=0, hence arrived at this:

I_L(t) = 6mA(1 - exp(-100000t))

i can't figure out how I_o came about.

can someone come it my rescue and tell me how the I₀ came into play.

Kind Regards,

 

[php]

anyone to help?

 

[nlightner]

I can provide some guidance on how to solve this transient analysis problem. It appears that you have correctly solved for the current in the inductor, IL(t), in terms of time. However, it is important to note that the current in the inductor is not the same as the current through the source, which is what I0 represents. To solve for I0, you will need to use Kirchhoff's laws and apply them to the circuit at t=0. This means that you will need to consider the initial conditions of the circuit, including the initial voltage across the inductor (which can be found using the current you calculated) and the initial voltage across the resistor. By applying Kirchhoff's laws, you should be able to solve for I0. I recommend reviewing your notes or textbook on how to apply Kirchhoff's laws to circuits with inductors to help you solve for I0. I hope this helps and good luck with your problem!