What am I doing wrong in calculating the capacitance of an air-filled capacitor?

[AdKo]

My answer is off by 10^-2!

Homework Statement

An air-filled capacitor consists of two parallel plates, each with an area of 7.60cm^2 and separated by a distance of 1.8mm. If a 20 V potential difference is applied to these plates, calculate the capacitance.

Homework Equations

$$C=\epsilon_{0}\frac{A}{d}$$

The Attempt at a Solution

$$C=\epsilon_{0}\frac{A}{d}$$
$$=(8.85*10^-12)\frac{0.076m^2}{0.0018m}$$
=3.74*10^-10F

Book answer: 3.74*10^-12? What am I doing wrong? thanks.

 

[cristo]

Check your conversion from cm² to m².

 

[AdKo]

Check your conversion from cm² to m².

I don't get it. Do you need to count the ^2 too? How do you convert that?
I know that 7.6cm=.076m..

 

[cristo]

You know that there are 100 cm in a metre, so in a metre-squared, there are 100²=10 000cm.

 

[AdKo]

You know that there are 100 cm in a metre, so in a metre-squared, there are 100²=10 000cm.

But isn't cm square also? Or is it like (xm)^2 and you need to distribute so x^2m^2? Cm^2 already has the magnitude distributed right? Is that the reason?

 

[AdKo]

By the way, I've always ignored all of the powers that came after the units.. But I guess that's because I never converted them. I really need this explained =/

 

[AdKo]

Wait is it like this?:

$$\frac{5cm^2}{1}*\frac{1m}{(100cm)^2}$$

$$=\frac{5cm^2}{1}*\frac{1m}{10000cm^2}$$

?? -- I guess that would mean the 5cm^2 already had its square root distibuted? Am I thinking the right way?

 

[cristo]

But isn't cm square also? Or is it like (xm)^2 and you need to distribute so x^2m^2? Cm^2 already has the magnitude distributed right? Is that the reason?

I don't really know what you mean here. The unit is centimetre squared, and we are trying to convert it to metres squared (we can do this, since they are both units of area)

By the way, I've always ignored all of the powers that came after the units.. But I guess that's because I never converted them. I really need this explained =/

OK, well if you were measuring the length of something, then a valid answer would be, say, 10cm, since the centimetre is a unit of length. We can convert this to metres by dividing by 100, since the metre is a unit of length also.

Now, suppose we have a measurement in centimetres squared. Now, this is a unit of area: as an example, if we draw a square on paper with sides 5cm, then the total area will be 5x5=25cm².

So, to convert from centimetres squared to metres squared, consider drawing a square of sides 1m on paper. Since 1m=100cm, we know that each side is 100cm long. But, what is the total area in centimetres squared? Well, area=lengthxheight, and so for a square of sides 100cm, it is area 10 000cm².

So, we see that a square of area 1m² has area 10 000cm² i.e. 1m²=10 000cm².

 

[AdKo]

I don't really know what you mean here. The unit is centimetre squared, and we are trying to convert it to metres squared (we can do this, since they are both units of area)



OK, well if you were measuring the length of something, then a valid answer would be, say, 10cm, since the centimetre is a unit of length. We can convert this to metres by dividing by 100, since the metre is a unit of length also.

Now, suppose we have a measurement in centimetres squared. Now, this is a unit of area: as an example, if we draw a square on paper with sides 5cm, then the total area will be 5x5=25cm².

Now, to convert from centimetres squared to metres squared, consider drawing a square of sides 1m on paper. Since 1m=100cm, we know that each side is 100cm long. But, what is the total area in centimetres squared? Well, area=lengthxheight, and so for a square of sides 100cm, it is area 10 000cm².

So, we see that a square of area 1m² has area 10 000cm² i.e. 1m²=10 000cm².

I think I totally understand now! Your explanation was great. So would this be correct??

(l_ is the base + height)

l_ :1mx1m=1m^2

l_ :100cmx100xcm=10000cm^2

 

[cristo]

I think I totally understand now! Your explanation was great. So would this be correct??

(l_ is the base x height)

l_ :1mx1m=1m^2

l_ :100cmx100xcm=10000cm^2

With the slight correction, that base x height is the area, then yes, you are correct.

 

[AdKo]

With the slight correction, that base x height is the area, then yes, you are correct.

Alright, thanks a lot!