# A charge of #25 C# is passing through points A and B on a circuit. If the charge's electric potential changes from #32 J# to #14 J#, what is the voltage between points A and B?

##### 2 Answers

Voltage between points A and B is

#### Explanation:

Voltage can be thought of as electrical potential energy per unit charge.

So we say, in absolute terms (which don't exist), that:

For a constant charge, and **a change in** potential aka Voltage (and potential energy), we see therefore that:

The voltage between points A and B is, therefore,

Point A is higher in potential than point B by 0.72 volts.

#### Explanation:

The relation between electric potential energy change and potential (voltage) change is

where W is the change in potential energy (the work done on or by the charge as it moves from A to B) and V is the potential difference between A and B. q is the amount of charge transported.

In this case, the potential energy changes from 32 J to 14 J, which is a change of 18 J. This is the quantity that matters. It's a bit like saying "if I climb from the 14th floor to the 32nd floor of a building, I have climbed 18 floors." Where I start and where I finish is not important; what matters is the difference of 18 floors between the starting and ending points.

So,

The combination of units "joules per coulomb" is known as the volt. So, our final answer is a difference of 0.72 volts between A and B.

Also, if the charge was positive, then since the potential energy decreased, the electric potential also must have decreased, meaning A is higher than B by 0.72 volts.

(It's the same as the floor example. If i find my potential energy has decreased as I go from one floor to the other, my starting point must have been higher than my ending point.)