Fig. 2.1 shows the current-voltage (I-V) characteristic obtained by a student for a filament lamp. She set up a circuit containing the lamp, a variable d.c....

Part (a) - Describing the I-V relationship [2 marks]

The current increases as the p.d. increases, but the rate of increase of current decreases at higher voltages. The graph curves, becoming less steep as the p.d. rises.

For full marks, both observations are needed: (1) current increases with p.d., and (2) the increase is not proportional (the curve flattens).

Part (b) - Why the graph is curved [2 marks]

As the current increases, more electrical energy is dissipated in the filament, raising its temperature. Metal filaments have the property that their resistance increases with temperature. Because the resistance rises, each additional volt produces a smaller increase in current than the one before, so the graph curves away from a straight line.

The two marking points are: (1) the filament gets hotter as current increases, and (2) resistance of a metal increases with temperature, preventing proportional current increase.

Part (c) - Resistance at 4.0 V [2 marks]

Read the current from the graph at V = 4.0 V: approximately \( I \approx 1.25 \) A (values between 1.2 and 1.3 A are acceptable).

\( R = \frac{V}{I} = \frac{4.0}{1.25} = 3.2 \; \Omega \)

The answer should be consistent with whatever value is read from the graph. Resistance at any point on the curve is found by dividing the voltage by the current at that point, not from the gradient.

Part (d) - Ohm's law [1 mark]

The filament lamp does not obey Ohm's law. Ohm's law states that current is proportional to p.d. at constant temperature, which would produce a straight line through the origin. The curved graph shows that the resistance changes with current (and hence temperature), so Ohm's law is not obeyed.