# Electric Potential Difference

The difference in the amount of electric potential energy between two points in an electric circuit is called ELECTRIC POTENTIAL DIFFERENCE or potential difference. Potential difference is known as voltage, which is equal to the work done per unit charge to move the charge between two points against static electric field.

Therefore,

`text(Voltage)=text(Work done)/text(Charge)`

Voltage or electric potential difference is denoted by **V**. Therefore;

`V=W/Q` -----------(1)

Where, W = work done and Q = Charge

## SI unit of potential difference

SI unit of electric potential difference is volt and denoted by **V**. This is named in honour of Italian Physicist **Alessandro Volta**.

`V=text(Joule)/text(Coulomb)=J/C`

Or, `V=J C^(-1)`

Since joule is the unit of work and coulomb is the unit of charge, 1 volt of electric potential difference is equal to the 1 joule of work to be done to move a charge of 1 coulomb from one point to another in an electric circuit. Therefore,

`1V=(1 text(Joule))/(1 text(Coulomb))=(1J)/(1C)`

**Voltmeter:** An apparatus to measure the potential difference or electric potential difference between two points in an electric circuit.

Example 1: Calculate the work done if a charge of 5 C moving across two point having potential difference equal to 15 V.

**Solution:** Given, potential difference (V) = 15 V

Charge (Q) = 5 C

Work done (W) =?

We know that, `V = W/Q`

Or, `W = V xx Q`

Or, `W = 15 V xx 5 C = 75 J`

Example 2: Calculate the work done to carry a charge of 3 C, if the potential difference between two points is 10 V.

**Solution:** Given, charge = 3 C

Potential difference between two points = 10V

Work done (W) =?

We know that, `V = W/Q`

Or, `W = V xx Q`

Or, `W = 10 V xx 3 C = 30 J`

Example 3: What potential difference is required to do 100 J of work to carry a charge of 10 C between two points?

**Solution:** Given, work done (W) = 100J

Charge (Q) = 10C

Potential difference (V) =?

We know that, `V = W/Q`

Or, `V = (100 J)/(10 C) = 10 V`

Example 4: Calculate the potential difference between two points, if 1500 J of work is done to carry a charge of 50C from one point to other?

**Solution:** Given, work done (W) = 1500J

Charge (Q) = 50C

Potential difference (V) =?

We know that, `V = W/Q`

Or, `V = (1500 J)/(50 C) = 30 V`

Example 5: 5000 J of work would is done to carry how much charge between two points having potential difference of 100 V?

**Solution:** Given, potential difference (V) = 100V

Work done (W) = 5000 J

Charge (Q) =?

We know that, `V = W/Q`

Or, `Q = W/V`

Or, `Q = (5000 J)/(100 V) = 50 C`

Example 6: To carry how much charge between two points having potential difference equal to 220 V, 1760 J of work is done?

**Solution:** Given, potential difference (V) = 220V

Work done (W) = 1760 J

Charge (Q) =?

We know that, `V = W/Q`

Or, `Q = W/V`

Or, `Q = (1760 J)/(220 V) = 8 C`

##### Symbols used in a Circuit diagram

Fig: Common Symbols of Circuit Diagram