# To double the energy stored by a capacitor, you should:

a) double the voltage
b) double the capacitance

WIth the equation U=(1/2)CV^2 doubling the voltage quadruples U and doubling the capacitance doubles U.

However if you double the capacitance in the expression (1/2)Q^2/C you half U instead.

Also, doubling the voltage doubles U in the equation (1/2)QV

So what's the reasoning behind this and where am I confusing myself?

gneill
Mentor
a) double the voltage
b) double the capacitance

WIth the equation U=(1/2)CV^2 doubling the voltage quadruples U and doubling the capacitance doubles U.

However if you double the capacitance in the expression (1/2)Q^2/C you half U instead.

Also, doubling the voltage doubles U in the equation (1/2)QV

So what's the reasoning behind this and where am I confusing myself?

Yeah, it's a bit tricky because each of the expressions for energy has behind it certain implications about what is varying and what remains constant. Just because a variable doesn't appear in the expression doesn't mean it doesn't change or have an impact. You have to think of the implied physical scenario when you 'wiggle' the variables in a given equation.

For a given capacitor Q = C*V always holds and specifies the effect on the "unseen" variable. So if you muck with one of the variables and hold another constant then by implication the third must change too.