Calculating Capacitance of Isolated Capacitor with Conductor Inserted

[voelkner]

Homework Statement

An isolated capacitor with capacitance C = 1 µF has a charge Q = 29 µC on its plates

A conductor is inserted into the capacitor with thickness of the conductor is 1/3 the thickness of the capacitor and is centered in between the plates of the capacitor.

What is the capacitance of the capacitor with the conductor in place?

Homework Equations

C = Q/V

V = E*d

The Attempt at a Solution

I've been trying this problem for hours. I know that since the capacitor is a conductor it makes the distance between the two plates smaller which means that the capacitance should therefore increase. I thought that since we now had two distances that were each 1/3 the original distance the capacitance would increase by a factor of 6 however this answer does not work. Can anyone help me?!?

 

[tiny-tim]

I thought that since we now had two distances that were each 1/3 the original distance the capacitance would increase by a factor of 6 however this answer does not work. Can anyone help me?!?

Hi voelkner!

6 = 3 + 3 … isn't that for capacitors in parallel?

these capacitors are in series.

 

[voelkner]

Would it then be 1/C?

 

[tiny-tim]

Would it then be 1/C?

1/C = 1/C₁ + 1/C₂