# 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

## 2 Answers

1st order differential equation, then solve using the integrating factor method: $$\frac{dv_c}{dt}\small +\frac{1}{C(100+t)}\large v_{c}\small =\frac{1}{C(100+t)}$$

Seems to me that you can write the current as something like

$$I(t) = (V(t) - Vc(t))/(100+t)$$ and $$Vc(t) = K + \int {I(t)/C}dt$$ Where K is the initial voltage state of the cap.

This from basic circuit theory ( Q=CV, I=dQ/dt and I = V/R and such) what is the problem?

• I was trying to write KVL equation on loop and solve it using simply making differential equation.So was getting differential equation with coefficients which are not constant.and was having difficulty in solving it, without laplace. while with laplace I was able to solve it. – Buzz bee Mar 5 '19 at 14:22