The method for finding the energy stored depends on the specific component or system. Let's focus on finding the energy stored in a capacitor, which is a common electrical component that stores energy in an electric field.
Energy Stored in a Capacitor
The energy stored in a capacitor can be determined using the following formulas, derived from the fundamental relationships between charge (Q), voltage (V), and capacitance (C):
- Ecap = (QV)/2
- Ecap = (CV^2)/2
- Ecap = (Q^2)/(2C)
Where:
- Ecap is the energy stored in the capacitor (in Joules).
- Q is the charge on the capacitor (in Coulombs).
- V is the voltage across the capacitor (in Volts).
- C is the capacitance of the capacitor (in Farads).
Essentially, you need to know at least two of the three variables (Q, V, and C) to calculate the energy stored in the capacitor.
When to use which formula:
Here's a breakdown of when to use each formula:
| Formula | When to Use |
|---|---|
| Ecap = (QV)/2 | When you know the charge and voltage. |
| Ecap = (CV^2)/2 | When you know the capacitance and voltage. |
| Ecap = (Q^2)/(2C) | When you know the charge and the capacitance. |
Example:
Let's say you have a capacitor with a capacitance of 2 Farads (C = 2 F) and a voltage of 10 Volts (V = 10 V) across it. To find the energy stored, you'd use the formula:
Ecap = (CV^2)/2 = (2 F (10 V)^2)/2 = (2 100)/2 = 100 Joules.
Therefore, the capacitor stores 100 Joules of energy.
Units:
Remember to use consistent units:
- Charge (Q) in Coulombs (C)
- Voltage (V) in Volts (V)
- Capacitance (C) in Farads (F)
- Energy (Ecap) will then be in Joules (J)
