What is the Area of a Capacitor Plate?

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In summary: Remember to check your units and use proper notation (e.g. use parentheses when necessary) to avoid errors. Great job!In summary, the capacitance can be calculated by dividing the charge by the voltage, and also by multiplying the permittivity of free space by the square of the side length of the parallel plates and dividing by the distance between the plates. In the given attempt at a solution, the distance value was incorrect and the plate area was incorrectly calculated by involving the square of the side length. The correct calculation for the plate area is to multiply the capacitance by the distance and divide by the permittivity of free space. After fixing the errors, the plate area was calculated to be 2 square meters.
  • #1
warnexus
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Homework Statement



platearea.jpg


Homework Equations


capacitance = charge/volt

capacitance = Esub0 (side of parallel plates^2)/(distance apart)

The Attempt at a Solution



capacitance = (3*10^-6 C)/(150v)
capacitance = 2 * 10 ^ - 8 F

2 * 10 ^ - 8 F = (8.85 * 10 ^ -12)(side of parallel plate) ^ 2/(.90 *10^-2)

side of parallel plate is 20 m ^ 2.
 
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  • #2
warnexus said:

Homework Statement



platearea.jpg


Homework Equations


capacitance = charge/volt

capacitance = Esub0 (side of parallel plates^2)/(distance apart)




The Attempt at a Solution



capacitance = (3*10^-6 C)/(150v)
capacitance = 2 * 10 ^ - 8 F

2 * 10 ^ - 8 F = (8.85 * 10 ^ -12)(side of parallel plate) ^ 2/(.90 *10^-2)
Your distance value doesn't look right; check your units conversion. Since you're looking for the plate area anyways, why involve the square of the side length when you can solve directly for the area?

Fix your d value and try again. Make sure that your result description and units match (you reported a side length in square meters before).
 
  • #3
gneill said:
Your distance value doesn't look right; check your units conversion. Since you're looking for the plate area anyways, why involve the square of the side length when you can solve directly for the area?

Fix your d value and try again. Make sure that your result description and units match (you reported a side length in square meters before).

oops milli is 10^ -3

i found my mistake. plate area = (capacitance)(distance)/(esub0)

plate area = (2*10^-8)(.90 * 10 ^-3)/ (8.85 * 10 ^ -12) = 2 m ^ 2 =]

thanks gneill
 
  • #4
warnexus said:
oops milli is 10^ -3

i found my mistake. plate area = (capacitance)(distance)/(esub0)

plate area = (2*10^-8)(.90 * 10 ^-3)/ (8.85 * 10 ^ -12) = 2 m ^ 2 =]

Yup, that looks better :smile:
 
  • #5


To find the area of the plate, we can rearrange the equation for capacitance to solve for the area:

Area = (capacitance * distance apart) / (Esub0)^(1/2)

Substituting in the values given, we get:

Area = (2 * 10^-8 F * 0.9 * 10^-2 m) / (8.85 * 10^-12 F/m)

= 2.03 * 10^-2 m^2

Therefore, the area of the plate is approximately 0.0203 square meters.
 

FAQ: What is the Area of a Capacitor Plate?

What is the formula for finding the area of a plate?

The formula for finding the area of a plate is length x width. This formula assumes that the plate is a rectangle or square shape. If the plate is a different shape, such as a circle, a different formula needs to be used.

What units are used to measure the area of a plate?

The area of a plate is typically measured in square units, such as square inches, square feet, or square meters. These units represent the amount of space that is covered by the plate's surface.

Do I need to know the exact measurements of the plate to find the area?

Yes, in order to accurately find the area of a plate, you will need to know the exact measurements of the length and width. This can be done by using a ruler or measuring tape.

Can the area of a plate be calculated if the plate is not a perfect shape?

Yes, the area of a plate can still be calculated even if the plate is not a perfect shape. This can be done by breaking the plate into smaller, more manageable shapes and finding the area of each shape. Then, the areas can be added together to find the total area of the plate.

Why is it important to find the area of a plate?

Finding the area of a plate is important for various reasons. It can help determine the amount of material needed to cover the plate, such as paint or fabric. It can also be useful in calculating the cost of the plate or determining how much food can fit on the plate.

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