How Do You Calculate Capacitance for Different Types of Capacitors?

[mmattson07]

Homework Statement

The plates of a spherical capacitor have radii 30.3 mm and 33.1 mm. (a) Calculate the capacitance in picofarads. (b) What must be the plate area in square centimeters of a parallel-plate capacitor with the same plate separation and capacitance?

Homework Equations

C= 4$$\Pi$$$$\epsilon$$(ab/b-a) (Spherical Capacitor)
C=$$\epsilon$$A/d (Parallel Plate)

The Attempt at a Solution

a)
I am having trouble with the conversion to pF. I know it's 10^-12.
=>C= 4$$\Pi$$$$\epsilon$$((.0303*.0331)/(.0331-.0303))=3.984e-11 F = .3984 pF ??

b) =>A=Cd/$$\epsilon$$ = 3.984e-11 F(.0331-.0303)/8.85e-12

Thanks!

 

[Dickfore]

3.984e-11 F = .3984 pF ??

You made a mistake in conversion:

$$10^{-11} \, \mathrm{F} = 10^{1 - 12} \, \mathrm{F} = 10^{1} \, 10^{-12} \, \mathrm{F} = 10 \, \mathrm{pF}$$

 

[mmattson07]

Still confused...how do I convert then? Is it 3.984e-12 pF??

 

[mmattson07]

Or 39.84 pF?

 

[Dickfore]

Or 39.84 pF?

yes.