# Solving RC circuits with impulse or unit step input by using convolution integral

I want to learn the solution of RC circuits by method of convolution with impulse response and input

and find zero state solution.However I couldn't understand clearly the using of the method. For example I have such question

and I wanted to use this method to solve this problem . I obtain impulse response of Vc and convolve with given input

as shown but I couldn't find desired answer.Can you give me insight ?

-Firstly You should find the impulse response of Vc for given impulses

differently.

-Then you know that capacitor acts like short circuit in impulse response .

-You find the impulsive current then find voltage by integrating the current in given t so you can find the impulse response.

-Secondly do the same thing for second input.

-For zero state solution you should convolve your first impulse response with first input waveform and second impulse response with second input waveform.

-Convolve 0 to t which you want to find zero state solution then add zero state solution to zero input solution.

I think this can be helpful.

• When I solve this question in that way , I couldn't find the correct answer.Because I solved this question by initial final voltage method and I found the correct answer in that way. – user158660 Dec 8 '17 at 10:51