Question

The temperature at which the tungsten filament of 12v and 36w lamp operates is 1730^0c. if the temperature coefficient of resistance of tungsten is 6 x 10^-3/k, find the resistance of the lamp at a room temperature of 20^0c

Answer 1

Answer on Question #48428-Physics-Molecular Physics-Thermodynamics

The temperature at which the tungsten filament of 12v and 36w lamp operates is $1730^{\wedge}0c$ . If the temperature coefficient of resistance of tungsten is $6 \times 10^{\wedge} - 3 / k$ , find the resistance of the lamp at a room temperature of $20^{\wedge}0c$

Solution

The resistance of the lamp at $1730{}^{\circ}\mathrm{C}$ is

$$R = \frac {V ^ {2}}{P} = \frac {(1 2 \mathrm {V}) ^ {2}}{3 6 \mathrm {W}} = 4 \mathrm {O h m}.$$

The resistance of the lamp at a room temperature of $20{}^{\circ}\mathrm{C}$ is

$$R _ {1} = R (1 + \alpha \Delta T) = 4 (1 + 6 \cdot 1 0 ^ {- 3} \cdot (1 7 3 0 - 2 0)) = 4 5 O h m.$$

Answer: 45 Ohm.

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