Question

5 The temperature at which the tungsten filament of a 12V and 36W lamp operates is
1730 o C 1730oC
. If the temperature coefficient of resistance of tungsten is
6×10 −3 /K 6×10−3/K
, find the resistance of the lamp at a room temperature of
20 o C 20oC



10.00Ω 10.00Ω


0.45Ω 0.45Ω


0.39Ω 0.39Ω


4.00Ω 4.00Ω

Answer 1

Answer on Question #58259-Engineering-Mechanical Engineering

The temperature at which the tungsten filament of a 12V and 36W lamp operates is 1730°C. If the temperature coefficient of resistance of tungsten is $6 \times 10^{-3} / \mathrm{K}$, find the resistance of the lamp at a room temperature of 20 o C.

10.00Ω

0.45Ω

0.39Ω

4.00Ω

Solution

$$P = \frac{U^2}{R} \rightarrow R = \frac{U^2}{P}.$$

The dependence resistance on the temperature is given by the formula

$$R = R_0 (1 + \alpha \Delta T)$$

In our case:

$$R = R_0 (1 + \alpha \Delta T) \rightarrow \frac{U^2}{P} = R_0 (1 + \alpha \Delta T) = \frac{12^2}{36} \left(1 + 6 \cdot 10^{-3} \cdot (20 - 1730)\right) = R_0 = \frac{U^2}{P (1 + \alpha \Delta T)} = \frac{12^2}{36 \left(1 + 6 \cdot 10^{-3} \cdot (1730 - 20)\right)} = 0.36\Omega$$

Answer: 0.36Ω.

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