In any fair investigation you change one quantity (the independent variable), measure one quantity that responds (the dependent variable) and keep everything else the same (the controlled variables). Questions on this appear in practical-style and planning questions in physics investigations and explanations.
What does each word mean?
The independent variable is the one you decide to change. The dependent variable is the one that depends on it, so you measure it each time. Controlled variables are the other quantities that could affect the result, so you keep them constant.
The reason is fairness. If two things change at once, you cannot say which one caused the change in your results.
How do you pick them out of a description?
- Find the question being asked: “how does A affect B?” Here A is independent and B is dependent.
- Ask what you would set before each trial. That is the independent variable.
- Ask what you would read from an instrument after each trial. That is the dependent variable.
- List what else could change the reading and say how you would hold each one constant.
Worked example
A student investigates how the length of a simple pendulum affects its time period. The question is “how does length affect the time period?” so A is length and B is time period.
Independent variable: length of the string, measured from the pivot to the centre of the bob, set to 20, 40, 60, 80 and 100 cm.
Dependent variable: the time period T in seconds. It is found by timing 20 swings and dividing by 20, which reduces the effect of reaction time.
Controlled variables:
- the same bob, so the mass is constant;
- the same small release angle each time, measured with a protractor;
- the same stopwatch and the same person timing, starting and stopping at the centre of the swing.
If the mass and the angle also changed, a difference in T could come from any of the three. Keeping them fixed means a change in T can be put down to length.
The mistake to watch for
A student writes: “The independent variable is the time, because it is what we measure.”
This reverses the roles. The word “independent” does not mean “important” or “measured”. It means the quantity the experimenter chooses.
You choose the lengths; the time depends on the lengths, so time is the dependent variable.
The correction is to ask “which one did I set?” before naming any variable.
Check yourself
1. A student hangs loads of 1 N to 5 N on a spring and measures the length of the spring each time. Name the independent and dependent variables and one controlled variable.
Show answer
Independent: the load in N. Dependent: the length (or extension) of the spring in cm. Controlled: the same spring each time (or the same ruler and zero position, or not stretching beyond the spring’s limit).
2. Three identical cups of hot water are covered with 0, 1 and 2 layers of cloth. Name two controlled variables for the investigation of cooling.
Show answer
Any two of: the same starting temperature, the same volume of water, the same time interval, the same room with no draught, the same type of cup and lid.
3. A student tests how the length of a wire affects its resistance but uses a thicker wire for each longer length. What has gone wrong?
Show answer
The thickness (cross-sectional area) is not controlled. Both length and area change, so the resistance results cannot be explained by length alone. The same wire of the same material and thickness should be used.
Where this leads next
Once you can name the variables, the next skill is deciding how to choose graph axes from a model. You can test the whole module with the investigations practice set. The bounds and rounding explainer helps when a recorded reading has been rounded.
If you can repeat definitions but still hesitate on a new set-up, that is the kind of reasoning gap our teachers work on in online one-to-one Physics tuition.