Potential difference and resistance

In a nutshell

Potential difference is the difference in the amount of energy that charge carriers possess between two points within a circuit. Resistance is the opposition to the movement of electrical charge through a circuit.

Equations

Variable definitions

Potential difference

Definition

Potential difference (or voltage) is the energy transferred per unit charge that passes between two points in a circuit. The potential difference across a component is the amount of energy transferred by that component per unit charge passing through it. Potential difference is needed to push the charge around the circuit.

The unit of potential difference is the volt. One volt is defined as one joule per coulomb. 

The following formula relates the potential difference across a component and the charge moved through it, to the energy that is transferred by that component:

​$$energy \space transferred = charge \space flow\times potential \space difference$$​​

​$$E = Q \times V$$

Potential difference can be measured by placing a voltmeter in parallel with a component in a circuit.

Resistance

Resistance is the opposition to the movement of electrical charge through a circuit or component. The resistance of an electrical component can be found by measuring the current flowing through it and the potential difference across it. 

The following equation can be rearranged to calculate the resistance of a component, if both the current and potential difference are known:

​$$potential \space difference = current \times resistance$$

$$V = I \times R$$

This equation is known as Ohm's Law.

Example

A $$6 \space \Omega$$ resistor in a circuit has a potential difference of $$7.5 \space V$$ across it. What is the current through the resistor?

First, write out the quantities needed and make sure they are in the correct form:

$$R = 6 \space \Omega$$​​

​$$V = 7.5 \space V$$​​

​

Next, write down the equation you need to use:

$$V = I \times R$$

$$I = \frac{V}{R}$$

Then, substitute the values into the equation:

$$I = \frac{7.5}{6}$$

Don't forget to include your units:

$$1.25 \space A$$​​

There is $$\underline{1.25 \space A}$$ of current flowing through the resistor.