Question

20 The temperature at which the tungsten filament of a 12 V and 36W lamp operates is
1730o
C. If the temperature coefficient of resistance of tungsten is
6×10−3
/K, find the resistance of the lamp at a room temperature of 20oC
10.00Ω
0.45Ω
0.39Ω
4.00Ω

Answer 1

Answer on Question #52083, Physics, Field Theory

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

10.00Ω

0.45Ω

0.39Ω

4.00Ω

Solution

Resistance at 1730°C

$$R(t = 1730{}^{\circ}C) = \frac{U^2}{P} = \frac{(12V)^2}{36W} = 4\Omega$$

Resistance versus of temperature

$$R(t) = R_0 (1 + \alpha t)$$

where $R_0$ is the resistance at zero degrees Celsius; $\alpha = 6 \cdot 10^{-3} K^{-1}$ the temperature coefficient of resistance of tungsten.

Then

$$R(t = 20{}^{\circ}C) = R_0 (1 + \alpha \cdot 20{}^{\circ}C) = \frac{R(t = 1730{}^{\circ}C)}{(1 + \alpha \cdot 1730{}^{\circ}C)} (1 + \alpha \cdot +20{}^{\circ}C) = \frac{4(1 + 6 \cdot 10^{-3} K^{-1} \cdot 20{}^{\circ}C)}{(1 + 6 \cdot 10^{-3} K^{-1} \cdot 1730{}^{\circ}C)} = 0.39\Omega$$

Answer: $R(t = 20{}^{\circ}C) = 0.39\Omega$

http://www.AssignmentExpert.com/