Dielectric in parallel plate capacitor

[seto6]

Homework Statement

Two capacitors, identical except for the dielectric material between their plates, are connected in parallel. One has a material with a material with a dielectric constant of 2, while the other has a material with a dielectric constant of 3. What is the dielectric constant that a material would need to have if the material were to replace the current dielectrics without changing the capacitance of the entire arrangement?

Homework Equations

C=Q/dV
C=(E_o)*A/s A is area , S is the separation

The Attempt at a Solution

since we need to keep the same capacitance, therefore we must not change the dielectric constant there we just add them up and we end up whit 2+3=5..
i tried this way didn't seem to work can anyone tell me where I'm going wrong! please!

 

[nickjer]

Why do you need to keep the same capacitance? What do you know about the total capacitance when capacitors are in series.

 

[seto6]

when they are in series they have the same Q there C=Q/V when you add all C you get
C_eq=((1/C_1)+(1/C_2))^-1

 

[nickjer]

I misread the problem. It seems it wants two capacitors and not one capacitor with the same dielectric for the final solution. It is still solved similarly. You solve for the total capacitance of your two initial capacitors in series, and then set it equal to the total capacitance of your two final capacitors which are identical and in series with each other. Then solve for the dielectric constant of your final capacitors.

You already know the formula for total capacitance of capacitors in series.

 

[seto6]

got it thanks