# Does the resistance of a filament lamp change?

Recently in a work book there has been a question to explain with the aid of a circuit diagram the method a student could use to investigate how the resistance of a single lamp changes with potential difference across the lamp. However I am unsure how to approach this question. Does the resistance of the filament lamp change with potential difference and current? If so, what is the relationship between them? How do I approach this tricky question? I have tried applying the equation to solve the problem but unfortunately to no avail

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

Any help and guidance would be incredibly helpful. ;)

Filaments are, quite deliberately by their construction, nonlinear resistors. That means their voltage-current characteristic doesn't follow the well-known Ohm's law $$U = R \cdot I$$ with a constant $$R$$, but rather $$R$$ varies with the applied voltage $$U$$ (or the current $$I$$, which is equivalent, but the question states resistance change with potential difference). So we could write $$U = R(U) \cdot I \qquad \text{or} \qquad R(U) =\frac{U}{I}$$

From here, you can try to continue yourself. How would you go on to find $$R(U)$$ from this expression? What experimental setup can you think of to get the data you need?

In general, resistance will increase for higher applied voltages. This increase is caused by the higher temperature of the filament, which—very roughly speaking—scatters electrons around more as they try to move through the medium.