potential difference

Voltage, also known as (electrical) potential difference, is the difference in electric potential between two points. It's unit is in \[V\], Voltage. In a static electric field, it corresponds to the work (joules) needed per unit of charge (coulombs) to move a positive test charge from the first point to the second point.

Since it is defined as work needed per unit charge, \[V=\frac{W}{Q}\]. With this we can define electric power in terms of electric current, \[P=\frac{W}{t}=\frac{W}{Q}\cdot \frac{Q}{t}=VI\]. Playing around with \[P=VI\] and \[V=IR\], we can turn \[P\] into \[P=VI=(IR)I=V \left( \frac{V}{R} \right)\].