Maximizing Wind Power: Calculating Capacitance for Energy Storage

In summary, the conversation discusses the use of a capacitor in a wind power plant to store energy during times of low wind speeds. The specific question is about determining the area of a parallel plate capacitor filled with air, with a separation distance of 3 meters, in order to store enough energy to power a town at 20 MW for three days. The equation for capacitance is mentioned and the person is asked to figure out the energy produced by the power plant in three days.
  • #1
Hotsuma
41
0

Homework Statement



A wind power plant will not produce as much energy when the wind slows down. In order to provide power during these time periods it is proposed to store some power when it is operating in high winds in a capacitor. If it is desired to store the energy to power a town at 20 MW (20*10^6) for three days, what is the area of a parallel plate capacitor (seperation, d, 3 meters) filled with air if the voltage is 50,000 V? Is there a way to reduce this size? Explain.

Homework Equations



K = 1.0006

The Attempt at a Solution



I cannot figure out where to start. I need to relate area to the capacitor, but I don't know if a Capacitor has an area l*w and then there is just a distance d seperating them or what. I'm lost and tired. Can someone help?
 
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  • #2
Start with the equation that gives the capacitance of a parallel plate, air-filled capacitor. What is that equation?
 
  • #3
[tex]C=k\cdot\frac{\epsilon_0A}{d}?[/tex]
 
  • #4
Thanks for the disappearing act; I was about to go to sleep.
 
  • #5
Correct capacitance expression. When you wake up, figure out how much energy the power plant produces in three days. All that energy is to be stored in the capacitor.
 

What is capacitance and how is it measured?

Capacitance is the ability of a capacitor to store electrical charge. It is measured in units of Farads (F) and is calculated by dividing the charge stored (Q) by the potential difference (V) across the capacitor, C = Q/V.

What is the energy stored in a capacitor and how is it calculated?

The energy stored in a capacitor is the amount of work required to charge the capacitor. It is calculated using the formula E = 1/2*CV^2, where C is the capacitance and V is the potential difference.

What is power in relation to capacitors?

Power is the rate at which energy is used or generated. In terms of capacitors, power is the rate at which the capacitor is charged or discharged. It is calculated using the formula P = IV, where I is the current flowing and V is the potential difference.

How does the type of dielectric material affect capacitance?

The type of dielectric material used in a capacitor affects its capacitance by changing the distance between the plates and the dielectric constant. The dielectric constant is a measure of how well the material can store electric charge. A higher dielectric constant will result in a higher capacitance.

How can capacitors be used to store energy and why is it beneficial?

Capacitors can be used to store energy by charging them and then using the stored energy to power devices. This is beneficial because capacitors can charge and discharge quickly, which makes them useful in applications where a sudden burst of power is needed, such as in camera flashes or electric vehicles.

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