Question

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?

Answer 1

Voltage between points A and B is `-0.72 V`.

Explanation:

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

So we say, in absolute terms (which don't exist), that: `V = U/Q`

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

`Delta V = (Delta U)/Q = (14-32)/(25) = -0.72 V`

The voltage between points A and B is, therefore, `-0.72 V`.

Answer 2

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

`W=qV`

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,

`18 J = 25C xx V`

`V= 18 J -: 25C = 0.72 J/C`

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.)