Find Energy stored in System of capacitors

[silkyjohnson]

Homework Statement

I have a system of capacitors set up in a combination of parallel and series connections. The first question(part a) asks me to find the total capacitance of the combination. The second question(part b) asks me to find the total energy stored in the system of capacitors.

They give me all the capacitances of each capacitor in the combination as well as the emf voltage.

So I got part A, no problem.

I think I did part B right but I just want to make sure I'm not oversimplifying things.

Homework Equations

Basically to find the total energy stored in the system, I used the equation U = (1/2)CV^2. I plugged in the value I found for part A into C, and used the given emf voltage.

(from part A) C = .75uF
(given emf) V = 1V

The Attempt at a Solution

So plugging those values into the equation, I got U = .375 uJ as my answer.

Now I am just wondering, is that all I do? At first I thought that maybe I had to figure out the energy stored for every capacitor individually, then add it all up... but after a while it just occurred to me to use the above equation for U.

I feel that I am correct, but I'm just hoping I can get some confirmation, or some help if I am wrong?

Thanks guys!

 

[rl.bhat]

Hi silkyjojnson, welcome to PF.
Your answer is correct.

 

[tomcue]

Your approach is correct. To find the total energy stored in a system of capacitors, you can use the equation U = (1/2)CV^2, where C is the total capacitance of the system and V is the voltage across the system. In this case, you correctly used the value for C that you found in part A and the given emf voltage to find the total energy stored in the system. There is no need to calculate the energy stored in each individual capacitor and then add them up, as long as you have the total capacitance and voltage for the entire system. Therefore, your answer of U = .375 uJ is correct.