Question

The tungsten filament of bulb has resistance equal to 18Ω at 27°C temperature 0.25 A of current flows, when 45V is connected to it If α = 4.5 ×10^–3K^–1 for a tungsten then find the temperature of the filament. 

(A) 2160 K 

(B) 1800 K 

(C) 2070 K 

(D) 2300 K

Answer 1

The correct option (D) 2300 K

Explanation:

given: I = 0.25A when V = 45V

∴ R = (V/I) = {45/(0.25)} = 180Ω

 R = R_o [1 + α (θ – θ_o)]

at θ_o  = 27°c = 273 + 27 = 300K, R_o = 18Ω, θ is filament temperature

∴ 180 = 18 [1 + α (θ – 300)]

∴ 10 – 1  = α(θ – 300)

(9/α) = θ – 300

∴ θ = 300 + (9/α) = 300 + {9/(4.5 × 10^–3)}

= 300 + 2000

θ = 2300K