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Cylinder capacitance question

Hi there

I posted this in maths, but think it might be more suitable here.

Please might anyone be able to advise me how to solve this problem in regard to the following cylinder? Dimensions L = 10-2 m, d = 10-3 m and D = 2 × 10-3 m.

I've been given the formula

Cm = (Capacitance/unit area ) x (surface area)

And have been asked to answer this question:

Calculate the capacitance of the outer curved surface if the material has:
Capacitance/surface area = 1.2 x 10-5 Fm2.
[Hint:]

I'm not sure how to go about this. Should I multiply 1.2 x 10-5 Fm2 by 2 pi r h (the surface area of the outer curved surface) to answer the question?

Please might anyone be able to advise me?

Thank you very much

Reply 1

Stonebridge

Yes.
You need the total outer surface area of the cylinder. Then multiply it by the capacitance per unit area, which is given.

Reply 2

Ggdf

Original post by Stonebridge

Yes.
You need the total outer surface area of the cylinder. Then multiply it by the capacitance per unit area, which is given.

Thank you very much, Stonebridge!

Reply 3

Ggdf

Original post by Stonebridge

Yes.
You need the total outer surface area of the cylinder. Then multiply it by the capacitance per unit area, which is given.

Hi Stonebridge

Do you think I've calculated this correctly?

1.2 x 10-5 Fm2 x 2.pi.r.l = (1.2E-5) x (2)(pi)(1E-3)(10E-2) = 7.5E-9F

Thank you

Reply 4

Ggdf

Original post by Ggdf

Hi Stonebridge

Do you think I've calculated this correctly?

1.2 x 10-5 Fm2 x 2.pi.r.l = (1.2E-5) x (2)(pi)(1E-3)(10E-2) = 7.5E-9F

Thank you

I'm unsure because I did the calculation assuming that length represented height in 2.pi.r.h. so I therefore did 2.pi.r.l. Was this incorrect?

Thank you very much

Reply 5

Stonebridge

The calculation is set up correctly but I get 10^-10 at the end not 10^-9

Is the length L =10^-2m?

Just check the figures and the calculation.

Reply 6

Ggdf

Original post by Stonebridge

The calculation is set up correctly but I get 10^-10 at the end not 10^-9

Is the length L =10^-2m?

Just check the figures and the calculation.

Thank you for your reply.

I've tried it again, but am still getting 10E-9. I'm not sure where I'm making a mistake.

The length is 10E-2m. I thought to calculate surface area by 2.pi.r.h, but then realised I have length not height.

Reply 7

Stonebridge

Original post by Ggdf

It could be you are using the calculator incorrectly.

10^-10 is entered as 1 exp -10 ( 1 x 10^-10)
Are you sure you are not incorrectly entering 10 x 10-10?
This would give the incorrect 10^-9

Reply 8

Ggdf

Original post by Stonebridge

It could be you are using the calculator incorrectly.

10^-10 is entered as 1 exp -10 ( 1 x 10^-10)
Are you sure you are not incorrectly entering 10 x 10-10?
This would give the incorrect 10^-9

Thank you for your help.

This is what I'm doing on the calculator:

calc 1.jpg

I'm not sure where I'm going wrong.

Reply 9

Stonebridge

Original post by Ggdf

Thank you for your help.

This is what I'm doing on the calculator:

calc 1.jpg

I'm not sure where I'm going wrong.

It's the last term that's entered incorrectly.

10^-2 is entered as 1 E -2 not 10 E-2

1 E -2 translates to 1 x 10^-2
10 E -2 translates as 10 x 10^-2

This is why you get 10^-9 instead of 10^-10

It's a common mistake in calculator usage.

Reply 10

Ggdf

Original post by Stonebridge

Thank you very much for pointing this out for me, I really appreciate it!

Reply 11

Ggdf

Original post by Stonebridge

Hi Stonebridge

Sorry to bring this up again. I had a look at the last calculator photo, and it seems that I have entered 10E-2 rather than 1E-2. Is it definitely the final term that is entered incorrectly?

Thank you

Reply 12

Stonebridge

Original post by Ggdf

Yes. The last term is entered incorrectly, as I said in my previous post.

If you have 10^-2

you should enter it as

1 E -2
which means
1 x 10^-2

If, as you have done, you enter

10 E -2
the calculator takes this as

10 x 10^-2