Question

The temperature at which the tungsten filament of a 12V and 36W lamp operates is 1730 Degrees Celsius. If the temperature coefficient of resistance of tungsten is 610^−3/K, find the resistance of the lamp at a room temperature of 20 Degrees Celsius.

(A) 10.00 ohms

(B) 0.45 ohms

(C) 0.39 ohms

(D) 4.00 ohms

Answer 1

Question#8520

The temperature at which the tungsten filament of a 12V and 36W lamp operates is 1730 Degrees Celsius. If the temperature coefficient of resistance of tungsten is $610{}^{\circ} \mathrm{C} / \mathrm{K}$, find the resistance of the lamp at a room temperature of 20 Degrees Celsius.

(A) 10.00 ohms

(B) 0.45 ohms

(C) 0.39 ohms

(D) 4.00 ohms

Solution:

Let:

$$U = 12V, \ P = 36W, \ T1 = 1730{}^{\circ}C, \ T2 = 20{}^{\circ}C, \ \alpha = 6 \cdot 10^{-3} \ \mathrm{K}^{-1}$$ $$R2 = ?$$

Find resistance of a lamp at $1730{}^{\circ}C$

$$P = I U, \ I = \frac{U}{R}$$ $$P = \frac{U^2}{R}$$ $$R = \frac{U^2}{P}$$ $$R1 = \frac{12^2}{36} = 4 \ \mathrm{ohms}$$

Dependence of resistance on temperature is:

$$R1 = R2(1 + \alpha \Delta T) =>$$ $$R2 = \frac{R1}{1 + \alpha \Delta T}$$ $$\Delta T = T1 - T2 = 1710{}^{\circ}C$$ $$R2 = \frac{4}{1 + 6 \cdot 10^{-3} \cdot 1710} = 0.36 \ \mathrm{ohms}$$

Answer: "C" (nearest value) Resistance is: 0.36 ohms