# Homework Help: My answer is off by 10^-2

1. Feb 18, 2007

My answer is off by 10^-2!!

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
$$C=\epsilon_{0}\frac{A}{d}$$

3. 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.

2. Feb 18, 2007

### cristo

Staff Emeritus
Check your conversion from cm2 to m2.

3. Feb 18, 2007

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

4. Feb 18, 2007

### cristo

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

5. Feb 18, 2007

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?

6. Feb 18, 2007

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 =/

7. Feb 18, 2007

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?

8. Feb 18, 2007

### cristo

Staff Emeritus
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.

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.

Last edited: Feb 18, 2007
9. Feb 18, 2007

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

10. Feb 18, 2007

### cristo

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

11. Feb 18, 2007

Alright, thanks a lot!