Question

A parallel-plate vacuum capacitor has 8.38 J of energy stored in it. The separation between the plates is 2.30 mm. If the separation is decreased to 1.15 mm, what is the energy stored (a) if the capacitor is disconnected from the potential source so the charge on the plates remains constant, and (b) if the capacitor remains connected to the potential source so the potential difference between the plates remains constant

Answer 1

Step-by-step explanation:

plate separation = 2.3 x 10⁻³ m

capacity C₁ = ε A / d

= ε A / 2.3 x 10⁻³

C₂ = ε A / 1.15 x 10⁻³

`(C_2)/(C_1)` =
`(2.3)/(1.15)`

a ) when charge remains constant

energy =
`(q^2)/(2C)`

q is charge and C is capacity

energy stored initially E₁=
`(q^2)/(2C_1)`

energy stored finally E₂ =
`(q^2)/(2C_2)`

`(E_1)/(E_2) = (C_2)/(C_1)` =
`(2.3)/(1.15)`

`E_2` =
`(1.15)/(2.3 ) * E_1`

=
`(1.15)/(2.3 ) * 8.38`

= 4.19 J

b )

In this case potential diff remains constant

energy of capacitor = 1/2 C V²

energy is proportional to capacity as V is constant .

`(E_2)/(E_1) = (C_2)/(C_1)`

`(E_2)/(8.38) = (2.3)/(1.15)`

`E_2` = 16.76 .