I have a physics problem where I used two different formulas to solve the answer. Why does this work?
A certain capacitor stores 35 mJ of energy when charged to 90 V.
How much would it store when charged to 30 V?
A: 3.889 mJ
What is it's capacitance?
A: 8.64 x 10^-6 F
I combined Vq=U and q=CV to get U=CV^2. I then noticed in my textbook that the actual equation is U=0.5C(V^2). Indeed, the correct answer for Capacitance can only be found from the formula in my textbook, and the formula that I derived is actually the same thing, only it just solves for 0.5C. My question is: why does my formula solve for 0.5C and not just C, since I manipulated strictly units and not any coefficients? If you look at the two formulas I combined, there is no 0.5 involved. Why is it that the end, it's randomly there, where is 0.5 coming from? Thanks for any intuition here!
A certain capacitor stores 35 mJ of energy when charged to 90 V.
How much would it store when charged to 30 V?
A: 3.889 mJ
What is it's capacitance?
A: 8.64 x 10^-6 F
I combined Vq=U and q=CV to get U=CV^2. I then noticed in my textbook that the actual equation is U=0.5C(V^2). Indeed, the correct answer for Capacitance can only be found from the formula in my textbook, and the formula that I derived is actually the same thing, only it just solves for 0.5C. My question is: why does my formula solve for 0.5C and not just C, since I manipulated strictly units and not any coefficients? If you look at the two formulas I combined, there is no 0.5 involved. Why is it that the end, it's randomly there, where is 0.5 coming from? Thanks for any intuition here!