Question

A parallel plate capacitor with plate separation d is connected to a battery. The capacitor is fully charged to Q Coulombs and a voltage of V. (C is the capacitance and U is the stored energy.) Answer the following questions regarding the capacitor charged by a battery. For each statement below, select True or False.

With the capacitor connected to the battery, decreasing d increases U. A: True B: False

After being disconnected from the battery, inserting a dielectric with κ will decrease V. A: True B: False

With the capacitor connected to the battery, increasing d increases C. A: True B: False

After being disconnected from the battery, inserting a dielectric with κ will increase C. A: True B: False

With the capacitor connected to the battery, increasing d decreases Q. A: True B: False

After being disconnected from the battery, inserting a dielectric with κ will increase U. A: True B: False

Answer 1

i

if k is the dielectric constant (k>1) C_o is capacitance in the vacuum and C is with dielectric

1)With the capacitor connected to the battery, decreasing d increases U: False

As d increases capacitance decreases and hence U decreases.

2) After being disconnected from the battery, inserting a dielectric with κ will decrease V.: True

As the dielectric is inserted capacitance increases, since capacitor is disconnected from battery charge remains same so by Q = CV so V reduces

3) With the capacitor connected to the battery, increasing d increases C: False

As d is increased capacitance reduces as per the formula

4) After being disconnected from the battery, inserting a dielectric with κ will increase C. True

As soon as the dielectric is inserted the capacitance will increase

5)With the capacitor connected to the battery, increasing d decreases Q.True

As d is increased capacitance reduces, since battery is connected V will remain same as battery potential

Q = CV , so as C reduces Q also reduces.

6) After being disconnected from the battery, inserting a dielectric with κ will increase U : False

As Dielectric is inserted C will increase, Since battery is disconnected charge Q remains constant

So U will reduce