Double Layer Parallel Plate Capacitor

In summary, the problem involves calculating the diameter of a second layer in a Parallel Plate Capacitor to prevent breakdown. The capacitor has a voltage of 180kV and two layers between the plates - one with Ep2=30kV/cm and the other with Ep1=50 kV/cm and a relative permittivity of 5. The relevant equations are U=U1+U2=\frac{Q}{e0*S}*(\frac{d1}{er1}+\frac{d2}{er2}), U1=E1d1, and U2=E2d2. To find the diameter, one approach is to calculate the critical Q and then use the formula E=\frac{Q}{e
  • #1
kilwan
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Homework Statement


d=10cm; U=180kV; er1=5; Ep1=50 kV/cm; Ep2=30 kV/cm; Ep=breakdown strength.
So you have a Parallel Plate Capacitor with two layers between the plates. One is air and it has the Ep2=30kV/cm, the other one has a Ep1=50 kV/cm and a relative permittivity of 5. The capacitor is on a voltage of 180k and you have to calculate the diameter of the second layer (with the Ep1) so that it doesn't come to an breakdown.

Homework Equations


U=U1+U2=[tex]\frac{Q}{e0*S}[/tex]*([tex]\frac{d1}{er1}[/tex]+[tex]\frac{d2}{er2}[/tex])
U1=E1d1
U2=E2d2

The Attempt at a Solution


Witch ever formula i use i end up have to many unknown variables. But i think i should calculate the critical Q and then get the S or the out of the formula for the eletric field of the layer.
 
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  • #2
E=\frac{Q}{e0*S} So i get E and then use U2=E2d2 to calculate d2. But i would like to get a different approach to the problem if someone could give me any tips.
 

1. What is a double layer parallel plate capacitor?

A double layer parallel plate capacitor is a type of capacitor that consists of two parallel metal plates separated by an insulating material called a dielectric. The capacitor is used to store electrical energy by creating an electric field between the plates.

2. How does a double layer parallel plate capacitor work?

When a voltage is applied to the capacitor, an electric field is created between the two plates. This causes a separation of charges, with positive charges accumulating on one plate and negative charges on the other. The dielectric material between the plates helps to maintain this charge separation, enabling the capacitor to store electrical energy.

3. What is the equation for the capacitance of a double layer parallel plate capacitor?

The capacitance of a double layer parallel plate capacitor is given by the equation C = εA/d, where C is the capacitance, ε is the permittivity of the dielectric material, A is the area of the plates, and d is the distance between the plates. This equation shows that the capacitance is directly proportional to the area of the plates and inversely proportional to the distance between them.

4. How does the distance between the plates affect the capacitance of a double layer parallel plate capacitor?

The distance between the plates has a direct impact on the capacitance of a double layer parallel plate capacitor. As the distance between the plates increases, the capacitance decreases. This is because the electric field between the plates weakens as the distance increases, resulting in a lower ability to store electrical energy.

5. What are the practical applications of double layer parallel plate capacitors?

Double layer parallel plate capacitors have a wide range of applications in various electronic and electrical systems. They are commonly used in power supplies, filters, timing circuits, and electronic devices such as computers and smartphones. They are also used in energy storage systems, such as battery backup systems and electric vehicles, due to their ability to store large amounts of energy in a small space.

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