A student investigated the variation of the current I flowing through a filament bulb for a range of different values of potential difference V - Leaving Cert Physics - Question 4 - 2005

The student varied the potential difference by adjusting the rheostat or potentiometer in the circuit. This device allows for gradual changes in voltage, providing different values of potential difference across the filament bulb while monitoring the resulting current.

The relationship between current and potential difference is not proportional because the graph shows a curve rather than a straight line. This indicates that as the potential difference increases, the rate of increase of current diminishes, suggesting a nonlinear relationship, typical of filament bulbs due to the increase in temperature as current flows.

At 1 V:

$R = \frac{V}{I} = \frac{1}{0.028} = 35.7 \Omega$

At 5 V:

$R = \frac{5}{0.091} = 54.9 \Omega$

To find the change in resistance:

$\text{Change in resistance} = 54.9 \Omega - 35.7 \Omega = 19.2 \Omega$

The resistance of the filament bulb increases as the current increases because the temperature of the filament rises. As the temperature increases, the atoms within the filament vibrate more, making it more difficult for electrons to flow through, thereby increasing resistance.