Capacitance 3 dielectrics sandwiched between two conductors.

[MostlyHarmless]

Find that capacitance of the system consisting of 3 dielectrics w/ length, l=1.0m, width, w= 1.0m and depth, d= 1.0 CM. ##k_1=1.5, k_2=2, k_3=2.5## *dimensions of conducting plates not given*

Equations: Capacitance, ##C= Q/{\delta}V##

Field in the dielectrics
##E={\frac{\sigma}{k{\epsilon}_0}}##

I've found the fields in each dielectric, and the potential difference in each, but I'm getting hung up there. I've gotten down to, ##|{\delta}V|=({\frac{Q}{A{\epsilon}_0}})({\frac{1}{k_1}}+{\frac{1}{k_2}}+{\frac{1}{k_3}})##

My problem is, the A refers to the area of the conducting plate, but as i pointed out, nothing is said concerning dimensions of those plates.

Is there another method that does not care about the area that I'm missing?

 

[mfb]

You can assume the plates have the same dimensions as width and length of the dielectric materials.

 

[MostlyHarmless]

That's what I thought, but the diagram provided clearly shows that conductors being larger than the dielectrics.

Is the portion that is the same dimension as the dielectrics the only portion if the conductor that has any effect?

 

[mfb]

That's what I thought, but the diagram provided clearly shows that conductors being larger than the dielectrics.

Can you show this diagram?

Is the portion that is the same dimension as the dielectrics the only portion if the conductor that has any effect?

No. For large k this is a good approximation (as you can neglect the air then), but your k-values are not large.

 

[Nickie]

As a scientist, it is important to always consider all the variables and factors in a given problem. In this case, the dimensions of the conducting plates are crucial in determining the capacitance of the system. As you have correctly pointed out, the area of the plates is needed in the equation for capacitance. Without this information, it is not possible to accurately calculate the capacitance.

One possible solution is to assume a standard size for the conducting plates, such as 1 square meter, and use that value in your calculations. However, this may not give an accurate result as the actual dimensions of the plates may differ.

Another approach could be to find the capacitance per unit area and then multiply it by the total area of the plates. This would require finding the electric field and potential difference in each dielectric, as you have already done, and then using the equation for capacitance per unit area, ##C/A= {\epsilon}_0/k##. This method would give a more accurate result as it takes into account the varying dielectric constants in the system.

In conclusion, it is important to have all the necessary information in order to accurately calculate the capacitance of a system. In this case, the dimensions of the conducting plates are needed and without them, it is not possible to find the exact capacitance.