How Does Partial Insertion of a Dielectric Affect Capacitor Voltage?

[vthang05]

A parallel-plate capacitor with only air between the plates is charged by connecting it to a battery. The capacitor is then disconnected from the battery, without any of the charge leaving the plates.

Part A:
A voltmeter reads 46.0 V when placed across the capacitor. When a dielectric is inserted between the plates, completely filling the space, the voltmeter reads 15.0 V. What is the dielectric constant of this material?

Part B:
What will the voltmeter read if the dielectric is now pulled partway out so it fills only one-third of the space between the plates?

I know how to do part A using K = Vo/V, But i do not know how to work the problem if it involve partial dielectric.Any helps or hints would be great thanks.

 

[OlderDan]

Think of the system as two separate capacitors. Are they arranged is series or in parallel?

 

[kyle8921]

Hi there,

Part A:
To solve for the dielectric constant, we can use the formula K = Vo/V, where K is the dielectric constant, Vo is the original voltage without the dielectric, and V is the voltage with the dielectric inserted. Plugging in the values given, we get:

K = 46.0 V / 15.0 V = 3.07

Therefore, the dielectric constant of the material is 3.07.

Part B:
To solve for the voltage with the dielectric partially inserted, we can use the formula V = Vo/K, where Vo is the original voltage without the dielectric and K is the dielectric constant. However, since only one-third of the space is filled, we need to adjust the value of K accordingly. The new K would be the average of the dielectric constant of air (which is 1) and the dielectric constant of the material (which we found to be 3.07 in Part A).

So, the new K would be (1 + 3.07) / 2 = 2.035. Plugging this into the formula, we get:

V = 46.0 V / 2.035 = 22.61 V

Therefore, the voltmeter would read 22.61 V if the dielectric is pulled partway out to fill only one-third of the space between the plates.

I hope this helps! Let me know if you have any further questions.