Fig. 1.1 shows a circuit with a variable resistor Rv in series with a lamp L and a cell providing 6.0 V. An ammeter measures current and a voltmeter measure...

(a) When \( R_v \) is at maximum, the ammeter reads:

\( I = 0.05 \text{ A} \) [1]

(b) Total resistance when \( R_v \) is at maximum:

\[ R_{\text{total}} = \frac{V_{\text{supply}}}{I} = \frac{6.0}{0.05} = 120 \; \Omega \]

[1]

This total includes both the variable resistor and the lamp in series.

(c) Resistance of the lamp at \( I = 0.05 \text{ A} \):

\[ R_{\text{lamp}} = \frac{V_L}{I} = \frac{0.5}{0.05} = 10 \; \Omega \]

[1]

(d) Resistance of the lamp at \( I = 0.50 \text{ A} \):

\[ R_{\text{lamp}} = \frac{V_L}{I} = \frac{5.8}{0.50} = 11.6 \; \Omega \]

[1]

(e) The lamp resistance is higher at the greater current (11.6 Ω vs 10 Ω) because the larger current heats the filament to a higher temperature. In metals, increased temperature causes lattice ions to vibrate more vigorously, increasing collisions with conduction electrons and raising the resistance. [1]

(f) Power dissipated in the lamp at each setting using \( P = IV \):

At \( R_v \) = maximum:

\[ P = 0.05 \times 0.5 = 0.025 \text{ W} \]

[1]

At \( R_v = 0 \):

\[ P = 0.50 \times 5.8 = 2.9 \text{ W} \]

[1]

The lamp is far brighter at the lower resistance setting because it dissipates over 100 times more power.

(g) The voltage across the lamp ranges from 0.5 V to 5.8 V. [1]

The variable resistor cannot produce exactly 0 V across the lamp (some current always flows), and the terminal p.d. cannot reach the full 6.0 V because of the cell's internal resistance.

(h) A variable resistor provides continuous, fine control over the current and voltage in the circuit without needing multiple power supplies or component swaps. A single adjustment sweeps through the full range smoothly. [1]

(i) Plan for plotting the full V-I characteristic: [2]

1. Starting with \( R_v \) at maximum, record the ammeter reading \( I \) and the voltmeter reading \( V_L \). [1]
2. Gradually decrease \( R_v \) in small steps, recording \( I \) and \( V_L \) at each step until \( R_v \) reaches zero. Plot \( V_L \) on the x-axis against \( I \) on the y-axis and draw a smooth curve of best fit through the points. [1]