Electric Potential and Potential Difference

What Makes Charge Flow? Potential Difference

Charges do not flow in a copper wire by themselves - just as water in a perfectly horizontal tube does not flow until there is a pressure difference. For charges to flow in a conductor, there must be a difference of electric pressure, called the potential difference, across it.

This potential difference is produced by a cell or a battery (one or more cells). The chemical action inside a cell maintains the potential difference across its terminals, even when no current flows. When connected in a circuit, this potential difference sets the charges in motion and drives the current. To keep the current flowing, the cell continually spends its stored chemical energy.

Defining Potential Difference: V = W/Q

The electric potential difference between two points is the work done to move a unit charge from one point to the other:

$$V = \frac{W}{Q}$$

The SI unit of potential difference is the volt (V), named after Alessandro Volta.

One volt is the potential difference between two points when 1 joule of work is done to move a charge of 1 coulomb from one point to the other:

$$1\ \text{V} = \frac{1\ \text{joule}}{1\ \text{coulomb}} = 1\ \text{J C}^{-1}$$

Potential difference is measured by a voltmeter, which is always connected in parallel across the two points between which the potential difference is to be measured.

Key Point: Ammeter → series; Voltmeter → parallel.

Solved Examples

Example 1: Work done to move a charge (NCERT 11.2)

How much work is done in moving a charge of 2 C across two points having a potential difference of 12 V?

Solution: $$W = V Q = 12\ \text{V} \times 2\ \text{C} = 24\ \text{J}$$

Example 2: Energy given by a battery

How much energy is given to each coulomb of charge passing through a 6 V battery?

Solution: $V = W/Q$, so for $Q = 1$ C, $W = VQ = 6\ \text{V} \times 1\ \text{C} = 6\ \text{J}$. Each coulomb gains 6 J of energy.

Example 3: Potential difference from work and charge

If 45 J of work is done to move 5 C of charge between two points, find the potential difference.

Solution: $$V = \frac{W}{Q} = \frac{45\ \text{J}}{5\ \text{C}} = 9\ \text{V}$$