# How to tackle circuit containing time variable resistor? simulate this circuit – Schematic created using CircuitLab

For instance above schematic find current as function of time in circuit above I studied it about months before and am not able to recall it neither i put it on notes {as I thought the solutions of these kind are too obvious} and not I am struck.I think I'll have to find laplace of each element.Consider zero state assumption.

• What do you need to find from this circuit? – DonFusili Mar 4 '19 at 10:52
• current with respect to time.Preferably using method of differential equation. – Buzz bee Mar 4 '19 at 11:09
• Can you please start listening to comments that tell you that you need to start showing us your work on these questions. From what I understand you are getting a lot of your questions from a book. If it is too advanced, you should try a different one, because most of your questions can be answered with a Google search. – MCG Mar 5 '19 at 13:03

1st order differential equation, then solve using the integrating factor method: $$\frac{dv_c}{dt}\small +\frac{1}{C(100+t)}\large v_{c}\small =\frac{1}{C(100+t)}$$
$$I(t) = (V(t) - Vc(t))/(100+t)$$ and $$Vc(t) = K + \int {I(t)/C}dt$$ Where K is the initial voltage state of the cap.