A dielectric with a dielectric constant of 3 is inserted into a parallel plate capacitor,filling one-half of the volume as shown in the figure.If the capacitance of the capacitor without the dielectric is C,what is the capacitance of the capacitor with the dielectric?

Question

Quizplus · Accepted Answer

The capacitance of a parallel plate capacitor is given by:
C = ε₀A/d
where ε₀ is the permittivity of free space, A is the area of the plates, and d is the distance between the plates.
When a dielectric is inserted between the plates, the capacitance increases by a factor of κ, the dielectric constant:
C' = κε₀A/d
In this case, the dielectric fills one-half of the volume, so its effect on the capacitance is reduced by a factor of 1/2. Therefore, the new capacitance is:
C'' = (1/2)C' = (1/2)(3ε₀A/d) = (3/2)ε₀A/d
This is equivalent to a capacitance increase of a factor of 3/2, or 1.5. Therefore,
C'' = 1.5C = 2C
So the correct answer is C) 2 C.

A Dielectric with a Dielectric Constant of 3 Is Inserted