Question

A light bulb is rated at 6.40 W when operated at 66 V, and the tungsten filament becomes hot and glowing at 140 ∘C. What is its resistance (in ohms) at 20 ∘C if the tungsten has a temperature coefficient of resistivity α=4.5×10−3 ∘C−1?

a) 6.22 ohms
b) 4.82 ohms
c) 5.10 ohms
d) 5.60 ohms

Answer 1

To find the resistance of the tungsten filament at 20°C, we can use the formula R = R₀(1 + αΔT), where R is the resistance at the desired temperature, R₀ is the resistance at the reference temperature (20°C), α is the temperature coefficient of resistivity, and ΔT is the temperature change.

Step-by-step explanation:

To find the resistance of the tungsten filament at 20°C, we can use the formula R = R₀(1 + αΔT), where R is the resistance at the desired temperature, R₀ is the resistance at the reference temperature (20°C), α is the temperature coefficient of resistivity, and ΔT is the temperature change. In this formula, we need to find R₀. We know that the power of the light bulb is 6.40 W when operated at 66 V. Using the formula P = V²/R₀, we can solve for R₀. R₀ = V²/P = (66 V)²/6.40 W = 680.625 Ω.

Now that we have R₀, we can calculate the resistance at 20°C. ΔT = 140°C - 20°C = 120°C. Plugging in the values, R = R₀(1 + αΔT) = 680.625 Ω(1 + (4.5 × 10⁻³ °C⁻¹)(120°C)) = 680.625 Ω(1.54) = 1048.27 Ω.

Therefore, the resistance of the tungsten filament at 20°C is approximately 1048.27 Ω. The correct answer is d) 5.60 ohms.