Potential difference V = W/Q
Work done for each coulomb of charge moved.
Moving charge takes work
Two points in a circuit carry a current. Work is done to move charge from the first point to the second. First 1 C is moved, using some work. Then 2 C are moved.
Compared with moving 1 C, how much work does moving 2 C need between the same two points?
What this lesson covers
The idea
The potential difference V between two points of a current-carrying circuit is the work done W to move a unit charge from one point to the other: V = W/Q.
Moving charge takes work
Two points in a circuit carry a current. Work is done to move charge from the first point to the second. First 1 C is moved, using some work. Then 2 C are moved.
Compared with moving 1 C, how much work does moving 2 C need between the same two points?
- Twice as much
- The same amount
- Half as much
Work per coulomb
Choose the work and the charge. The bar shows the work shared out over the coulombs.
A share for each coulomb
Each coloured block shows the work done on one coulomb. Its size is the potential difference V in volts, the unit you will meet next.
The potential difference V between two points of a current-carrying circuit is the work done W to move a unit charge from one point to the other: V = W/Q.
Notes
The potential difference V between two points is the work done W to move a unit charge between them: V = W/Q.
Check yourself
12 J of work is done to move 3 C of charge between two points. What is the potential difference, in V?
Answer: 4 V
V = W/Q = 12 J divided by 3 C = 4 V.
How much work is done to move 2 C of charge across two points whose potential difference is 12 V, in J?
Answer: 24 J
V = W/Q gives W = V × Q = 12 V × 2 C = 24 J.
Which expression gives the potential difference between two points?
The same charge is moved between two points in two cases. In case P the work done is 20 J and in case R it is 10 J. In which case is the potential difference larger?
- The charge moved divided by the work done. That is upside down. The potential difference is work done per unit charge, W divided by Q.
- The work done added to the charge moved. Work and charge are different quantities and are not added. The potential difference is W divided by Q.
- The work done divided by the charge moved — correct. Yes!
- Case P — correct. Yes!
- Case R. For the same charge, less work means a smaller potential difference, since V = W/Q.
- It is the same in both cases. V = W/Q, so for the same Q a different W gives a different V.