Why is the Energy in Capacitance Formula (CV^2)/2 Instead of QV?

In summary, energy in capacitance is the amount of energy stored in a capacitor, which can be calculated using the formula E = 1/2 * C * V^2. This energy can affect the performance of electronic devices by regulating voltage and providing temporary power. However, energy can also be lost in capacitance due to factors like heat dissipation and resistance in the circuit. To increase energy in capacitance, one can increase the capacitance or voltage by using larger capacitors or connecting multiple capacitors in series or parallel.
  • #1
semc
368
5
Hi, why is it that when u integrate V wrt to Q u get (CV^2)/2 instead of QV since voltage across is constant?
 
Physics news on Phys.org
  • #2
The voltage across the capacitor is not constant. The voltage delivered by the battery is constant, so the total energy from the battery is QV, but not all of that energy ends up in the capacitor.
 
  • #3


The reason for this is because the integral of voltage with respect to charge represents the area under the voltage vs. charge curve, which is equal to the energy stored in the capacitor. This area is calculated by taking the average voltage (V/2) and multiplying it by the total charge (Q), resulting in (CV^2)/2. This is known as the energy stored in a capacitor formula. It may seem counterintuitive that the voltage across the capacitor is constant, but the amount of charge that can be stored on the capacitor increases as the voltage increases, resulting in a non-linear relationship between voltage and charge. Hence, the energy stored in the capacitor is directly proportional to the square of the voltage and not just the voltage itself.
 

Related to Why is the Energy in Capacitance Formula (CV^2)/2 Instead of QV?

1. What is energy in capacitance?

Energy in capacitance refers to the amount of energy stored in a capacitor. A capacitor stores energy in the form of an electric field between two conductive plates, with the ability to release this energy when needed.

2. How is energy calculated in capacitance?

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

3. How does energy in capacitance affect the performance of electronic devices?

The amount of energy stored in a capacitor can affect the performance of electronic devices by impacting the voltage and current levels. Capacitors are commonly used in electronic circuits to regulate voltage and provide temporary power when needed.

4. Can energy be lost in capacitance?

Yes, energy can be lost in capacitance due to various factors such as heat dissipation, leakage current, and resistance in the circuit. This is known as capacitor loss and can affect the overall efficiency of the circuit.

5. How can energy in capacitance be increased?

The energy stored in a capacitor can be increased by increasing the capacitance or the voltage across the capacitor. This can be achieved by using larger capacitors or connecting multiple capacitors in series or parallel, respectively.

Similar threads

  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
993
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
2K
Replies
12
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
937
  • Introductory Physics Homework Help
Replies
4
Views
3K
  • Introductory Physics Homework Help
Replies
6
Views
830
Back
Top