A parallel-plate capacitor with only air between the plates is charged by connec

Question

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.

A) A voltmeter reads 46.0V when placed across the capacitor. When a dielectric is inserted between the plates, completely filling the space, the voltmeter reads 14.5V . What is the dielectric constant of this material?

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?

Explanation / Answer

A)

Capacitance directly proportional to dielectric

V = Q/C

V1/V2 = K2

46/14.5 = K2

k2 = 3.172

B)

when diectric is placed so that it fills only one third

then the two parts (one having dielectric, other withour dielectric) act like they are series

Q/C1 + Q/C2 = V

where V = 46

V = Q(3/KC + 3/2C) = V * (2.4456) = 112.5 V

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