Question

A capacitor stores 6.2 × 10–8 C of charge and 2.4 × 10–6 J of energy.

What is the capacitance of the capacitor?

8.0 × 10–10 F
1.6 × 10–9 F
4.6 × 10–5 F
9.3 × 10–5 F

Answer 1

9.3 × 10–5 F the same time

Answer 2

Answer:
8.0 * 10⁻¹⁰ F

Step-by-step explanation:
The energy, charge and capacitance can be related using the following formula:

`U = (1)/(2) * (Q^2)/(C)`

where:
U is the energy given = 2.4 * 10⁻⁶ J
Q is the charge given = 6.2 * 10⁻⁸ C
C is the value of capacitance we want to find

Substitute with the givens in the above equation to get the capacitance as follows:

`U = (1)/(2) * (Q^2)/(C)`

2.4 * 10⁻⁶ =
`(1)/(2) * ((6.2*10^-8)^2)/(C)`

(6.2 * 10⁻⁸)^2 = 2 * 2.4 * 10⁻⁶ * C

C =
`((6.2*10^-^8)^2)/(2*2.4*10^-^6) = 8.0 * 10^-^1^0 F`

Hope this helps :)