Electricity: Question 5

Worked solution

Step 1: Calculate the resistance at each data point

Using $R = V/I$ at each pair of readings:

Step 2: Interpret the trend

The resistance is not constant. It rises steadily from $5.00\,\Omega$ at $V = 1.00\text{ V}$ up to $10.0\,\Omega$ at $V = 4.00\text{ V}$. As $V$ (and hence $I$) increases, more electrical power $P = I^2R$ is dissipated as heat in the component, raising its temperature. A rising resistance with rising current/temperature is exactly the behaviour of a filament lamp: the increased thermal vibration of the metal ions in the filament scatters the free electrons more, increasing the resistivity and hence the resistance of the metal.

Step 3: Why the other options are wrong

• A: the resistance is only $5.00\,\Omega$ at the first data point. By the last point it has doubled to $10.0\,\Omega$, so it is not constant and the component is not ohmic.
• C: this describes the correct type of trend (a changing resistance linked to temperature) but the wrong direction. The data shows resistance increasing, not falling, so this does not match a thermistor (whose resistance would fall as it warmed up).
• D: resistance can always be calculated from a single pair of readings using $R = V/I$; it does not need to be constant (i.e. $I \propto V$) for $R$ to be well defined at each point.

Final answer

• The resistance rises from $5.00\,\Omega$ to $10.0\,\Omega$, consistent with a filament lamp, option B.