Resistance

Ohm's law tells us that for materials at a constant temperature, the potential difference, , and current, , are directly proportional to each other -> .

Directly proportional means that as one quantity increases, the other increases at the same rate - and vice versa. This means that if two variables (physics quantities) are directly proportional if:

-> When you double one, the other doubles or if you triple one, the other triples, etc

-> When you halve one, the other halves, or if you divide one by three, the other is divided by three also, etc

On a graph, we can tell if two variables are directly proportional if the graph:

• Is a straight line (the gradient/slope is constant)

• Passes through the origin (0,0)

Here, we can see a directly proportional relationship as the graph is a straight line through the origin, but we can also prove this with maths.

-> When the potential difference is , the current is . If the potential difference is doubled to the current will also double to .

-> When the potential difference is trippled to , the current is also tripled to .

Resistance is the ratio of potential difference to current in a component. This can be thought of as how much energy a coulomb of charge needs to move through a component per second. This is easiest to think about in terms of cycling. Cycling uphill: you are putting in lots of energy (high potential difference), but going slowly (low current) -> high resistance. Cycling downhill: you are not putting in much energy (low potential difference), but you are going fast (high current) -> low resistance.

Resistance is the opposition to the flow of current.

If the resistance of a circuit increases (harder for electrons to get through), the current will decrease. If the resistance of a circuit decreases (easier for electrons to get through), the current will increase. Resistance is measured in Ohms, written as .

Formula:

We can rearrange this to give us the definition of resistance, by dividing both sides by :

Example: If a bulb has a potential difference applied to it, and the current in the circuit is , we can use to calculate the resistance of the bulb:

Measuring Resistance

To measure resistance, we need to take measurements of both the current and potential difference, as, . We do this by using a voltmeter to measure potential difference, and an ammeter to measure current. For your exam, you need to know how to set a voltmeter and an ammeter up correctly to measure resistance. The voltmeter always goes in parallel with (across) the component it is measuring, the ammeter goes in series (next to).

If we do the experiment as shown, we will only get one value of pd and current. To plot a graph to check if Ohm's law is obeyed for the bulb (that the current and pd are directly proportional), we need multiple values. To do this, we need to add a variable resistor to the circuit, which is used to change the resistance so that we can get multiple readings (more on this below).

Variable resistors are any component that can change their resistance. Some can have their resistance changed manually, but some change resistance if the temperature changes or if the amount of light incident on them changes.

Thermistors are resistors that respond to changes in temperature. As the temperature increases, the resistance decreases. If the resistance decreases -> the current increases.

Light-dependent resistors (LDRs) are resistors that vary their resistance in response to light intensity. As the light intensity increases (more light), the resistance decreases.