Voltage of a capacitor as a function of time

I'm trying to code the voltage of a capacitor as a function of time.

I is an array of current values.

t is an array of time values with a time step of 1, with corresponding to the length of I: t = 0:length(I)-1

Vi is a constant.

C is a constant

V is an array of zeros, and it is the same length as I.

The formula is V(t=T) = (1/C)*sum(I) + Vi

where sum is from 0+ to T.

I have attempted several things. Here is where I am at:

for T = t

V = Vi + (1/C).*sum(I,(0:T));

end

This gives me an error for using zero in the summation.

When I do this:

for T = t

V = Vi + (1/C).*sum(I,(1:T));

end

It compiles.

Then I try to plot it:

figure(2),clf;

plot(t, V);

xlabel ('time');

ylabel('voltage');

title('voltage vs time');

The results clearly are not correct.

I then need to calculate the Power, which I know to be:

Power = V.*I

And the energy:

Energy = (1/2)*C.*V.^2;

And plot those as well.

Thank you in advance for the assistance!

Answer 1

[James Tursa]

Maybe the function you want is cumsum( ) instead of sum( )?

[Trey Blackwell]

I tried it,

for T = t

V = Vi + (1/C).*cumsum(I,(1:T));

end

It gave me:

Error using cumsum

Dimension argument must be a positive integer scalar within indexing range.

I'm not familiar enough with this function to know if I am doing it correctly. Can you elaborate a little bit?

[James Tursa]

I thought you were trying to incrementally sum up I. I.e., cumsum(I)

[Trey Blackwell]

The goal is to implement it into the formula I have listed for the voltage of a capacitor as a function of time:

V(t=T) = (1/C)*sum(I) + Vi

this is not my code, this is simply the fomula I am trying to implement. It needs to be a function of time, so I need to be able to sum I from 0+ to a given value of t.

[James Tursa]

Does the T correspond to the values in I? I.e., are you only interested in values of T that match the values in I? In which case simply use cumsum(I). Otherwise you will need to interpolate I for the T of interest. What is your situation?

[Trey Blackwell]

T is equal to the array t, which was created:

t = 0:length(I)-1;

Is what you are saying that I can just do this?

V = Vi + (1/C).*cumsum(I)

[James Tursa]

Yes, as long as the values in t correspond to the values in I.

[Trey Blackwell]

Looks like that worked! I will look a little more into that specific function to understand how it works. Thank you very much!