# Question 72abd

Jul 19, 2015

TIme needed: 198 years.

#### Explanation:

All you really need to know in order to be able to solve this problem is what exactly is a Coulomb.

A Coulomb is a unit of electric charge equivalent to the charge contained by $6.24 \cdot {10}^{18}$ electrons.

So, to get a total charge of 1 C, you need the body to give out a total of $6.24 \cdot {10}^{18}$ electrons.

You know that the body gives out ${10}^{9}$ electrons every second, so to reach the number of electrons contained in 1 C you'd need

6.24 * 10^(18)cancel("electrons") * "1 second"/(10^9cancel("electrons")) = 6.24 * 10^9"seconds"

To get a better understand of exactly how much time is needed, use a series of conversion factors to go from seconds to years

6.24 * 10^(9)cancel("s") * (1cancel("min"))/(60cancel("s")) * (1cancel("h"))/(60cancel("min")) * (1cancel("day"))/(24cancel("h")) * "1 year"/(365.24cancel("days")) = 0.000000198 * 10^(9)"years"

This is equivalent to

"time needed" = color(green)("198 years")#

SIDE NOTE I'll leave the answer rounded to three sig figs, just for good measure.