The plates of an air-filled parallel-plate capacitor with a plate area of 17.5 c

Question

The plates of an air-filled parallel-plate capacitor with a plate area of 17.5 cm^2 and a separation of 8.95 mm are charged to a 160-V potential difference. After the plates are disconnected from the source, a porcelain dielectric with x = 6.5 is inserted between the plates of the capacitor. (a)What is the charge on the capacitor before and after the dielectric is inserted? (b) What is the capacitance of the capacitor after the dielectric is inserted? (c) What is the potential difference between the plates of the capacitor after the dielectric is inserted? (d) What is the magnitude of the change in the energy stored in the capacitor after the dielectric is inserted?

Explanation / Answer

The capacitance C0 of the air filled capacitor is:

C0 = A0/d = [(17.5X10-4m2)(8.85X10-12F/m)]/[8.95X10-3m] = 1.73X10-12F

a) charge on the capacitor before dielectric in inserted is:

Qi = C0V = (1.73X10-12F)(160V) = 2.768X10-10C

charge on the capacitor after dielectric in inserted is:

Qf = Qi, because even though the capacitance increases after inserting dielectric, the charge will remain the same as before because there is no battery to provide the extra charge. Because the dielectric is introduced after disconnecting the source.

b) The capacitance of the capacitor after dielectric is intserted is

Cf = KC0 = 6.5C0 = 6.5(1.73X10-12F) = 11.245X10-12F, here K = dielectric constant of the dielectric

c) Since charge remains the same before and after dielectric in inserted, we have

Qf = Qi

CfVf = C0Vi

6.5C0Vf = C0(160V)

or Vf = 24.61V = potential difference after the dielectric is inserted.

d) Intital energy = (1/2)C0Vi2 = (0.5)(1.73X10-12F )(160V)2 = 2.214X10-8J

final energy = (1/2)CfVf2 = (1/2)6.5C0Vf2 = (0.5)(6.5)(1.73X10-12F )(24.61V)2 = 0.3405X10-8J

change in energy = 0.3405X10-8J - 2.214X10-8J = -1.8735X10-8J

So magnitude of change in energy = 1.8735X10-8J

This concludes the answers. If you find anything lacking please let me know.. I will resolve your query without delay....

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