A filament lamp gives measured (current in A, potential difference in V) pairs (0, 0), (0.10, 0.60), (0.20, 1.40), (0.30, 2.70), and (0.40, 4.80). Determine the static resistance at 0.40 A and estimate dynamic resistance between 0.30 and 0.40 A. Explain the graph shape microscopically, calculate power at 0.40 A, and design a safe circuit and procedure to collect the data without overheating the lamp between readings.

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Static resistance at 0.40 A is 12.0 Ω; interval dynamic resistance is 21.0 Ω; power is 1.92 W. Rising temperature increases lattice vibration and resistivity, so the slope grows. Static resistance at an operating point is V/I = 4.80/0.400 = 12.0 Ω. Dynamic resistance is the local gradient dV/dI. Over the final interval it is approximated by (4.80−2.70)/(0.40−0.30) = 21.0 Ω. As current rises, electrical heating raises filament temperature. Stronger lattice vibrations increase electron scattering and resistivity, so the V–I graph becomes progressively steeper. Power at 0.40 A is VI = (4.80)(0.400) = 1.92 W, consistent with I²R using the static resistance at that operating point. Use a low-voltage variable supply, series current-limiting resistor and switch, ammeter in series and voltmeter across the lamp. Increase current briefly, record simultaneous values, open the switch between readings, repeat in both directions, and do not exceed the rated current.

Diagnose a non-ohmic filament lamp

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Filament-lamp current–voltage observations

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Filament-lamp current–voltage observations — supplied values
Current / A	Potential difference / V
0	0
0.1	0.6
0.2	1.4
0.3	2.7
0.4	4.8