Calculations involving different Dielectrics and Capacitors

[as2528]

TL;DR Summary: Need dielectric constant for given capacitor

Given a 7.4 pF air-filled capacitor, you are asked to convert it to a capacitor that can store up to 7.4 mJ with a maximum potential difference of 652 V. Which dielectric in Table 25-1 should you use to fill the gap in the capacitor if you do not allow for a margin of error?

I did the following:

C=(k*e*A)/d and Q=C*V=>C=Q/V

So:

Q/V=(k*e*A)/d=>k=Q/V*d/(A*e)=>k=7.4*10^-6/652*7.4*10^-12=>k=8.7616*10^-20

The answer is 4.7, and uses the potential between capacitors formula. Why are the formulas I used wrong? It seems to me like it makes sense.

 

[hutchphd]

the potential between capacitors formula

What does that mean? What is Table 25-1?

 

[Steve4Physics]

In addition to what @hutchphd said:

Is the energy really 7.4mJ (millijoules) or did you mean 7.4μJ (microjoules)?

What formula relates energy (not charge) stored to C and V?

 

[as2528]

What does that mean? What is Table 25-1?

Table 25-1 was a table showing a few dielectric constants along with the materials they corresponded to. I was supposed to get 4.7 from the question, which was the part I failed on. On the table it said Pyrex was corresponding to that kappa.

 

[as2528]

In addition to what @hutchphd said:

Is the energy really 7.4mJ (millijoules) or did you mean 7.4μJ (microjoules)?

What formula relates energy (not charge) stored to C and V?

That was u=.5c*v^2. So I calculated with charge which causes the error?

 

[as2528]

That was u=.5c*v^2. So I calculated with charge which causes the error?

And it was the microjoules.

 

[Steve4Physics]

That was u=.5c*v^2.

That's the correct formula. But as far as I can see, you didn't use it.

So I calculated with charge which causes the error?

The charge (Q) is not needed. Try this:

Step 1: With the dielectric present, U(energy stored) =7.4μJ when V =652V. Use the formula U=½CV² to find C (the required capaicitance with the dielectric in place).

Step 2: Note that without the dielectric, the capacitance is 7.4pF. Use this and your result from Step 1 to find the dielectric constant.

 

[as2528]

That's the correct formula. But as far as I can see, you didn't use it.The charge (Q) is not needed. Try this:

Step 1: With the dielectric present, U(energy stored) =7.4μJ when V =652V. Use the formula U=½CV² to find C (the required capaicitance with the dielectric in place).

Step 2: Note that without the dielectric, the capacitance is 7.4pF. Use this and your result from Step 1 to find the dielectric constant.

Thank you! This cleared it up for me.