A parallel plate capacitor with plate separation d is connected to a battery. Th

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.

1) After being disconnected from the battery, increasing d increases U.
2) With the capacitor connected to the battery, inserting a dielectric with ? will decrease C.
3) After being disconnected from the battery, increasing d decreases V.
4) After being disconnected from the battery, inserting a dielectric with ? will increase V.
5) After being disconnected from the battery, decreasing d increases C.
6) After being disconnected from the battery, inserting a dielectric with ? will decrease U.

(please show work! thanks!)

Explanation / Answer

a)

true,

because V=q/C

V=q/(eo*A/d)

V=(q*d/eo*A)

here if d increases then V increases

b)

true,

because

C'=k*C

c)

False

here,

U=q^2/2C and U'=q^2/2C'

U'=q^2/2*(kC)

U'=U/k

U decreases

d)

false

v=q/C and v'=q/C'

v'=q/C'

=q/kC

v'=v/K

here, v' decreases

e)

true,

U=1/2*(q*V)

if d increases v increases

then U increases

f)

True,

C=eo*A/d

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