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

• Pi Face
In summary, doubling the voltage in an equation where U=(1/2)CV^2 will quadruple the energy (U) while doubling the capacitance will only double the energy. However, if you double the capacitance in the equation (1/2)Q^2/C, the energy will be halved instead. This can be confusing because each equation has implications for what is varying and what remains constant, so it's important to consider the implied physical scenario when changing variables.
Pi Face
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?

Pi Face said:
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.

## 1. How can I double the energy stored by a capacitor?

To double the energy stored by a capacitor, you can either increase the capacitance or the voltage. This can be achieved by using a larger capacitor or increasing the voltage across the capacitor.

## 2. What is the formula for calculating the energy stored in a capacitor?

The formula for calculating the energy stored in a capacitor is: E = 1/2 * C * V^2, where E is the energy in joules, C is the capacitance in farads, and V is the voltage in volts.

## 3. Can I double the energy stored by a capacitor by simply doubling the capacitance?

No, doubling the capacitance will not necessarily double the energy stored in a capacitor. The energy stored also depends on the voltage, so you will need to increase the voltage as well to double the energy stored.

## 4. Is it possible to double the energy stored by a capacitor without increasing the voltage or capacitance?

No, the energy stored in a capacitor is directly proportional to the voltage and capacitance. Therefore, to double the energy stored, you will need to increase one or both of these values.

## 5. What are the factors that affect the energy stored in a capacitor?

The energy stored in a capacitor is affected by the capacitance, voltage, and the dielectric material between the plates. The distance between the plates and the surface area of the plates also have an impact on the energy stored.

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