The filament of a certain lamp has a resistance that increases linearly with temperature. When a constant voltage is switched on, the initial current decreases until the filament reaches its steady-state temperature. The temperature coefficient of resistivity of the filament is 43 times 10^-3 K^-1. The final current through the filament is one - eighth the initial current. What is the change in temperature of the filament?

a. 30100 K

b. 378 K

c. 1627 K

d. 814 K

e. 1162 K

Question

Gator

Physics

24 March, 18:23

The filament of a certain lamp has a resistance that increases linearly with temperature. When a constant voltage is switched on, the initial current decreases until the filament reaches its steady-state temperature. The temperature coefficient of resistivity of the filament is 43 times 10^-3 K^-1. The final current through the filament is one - eighth the initial current. What is the change in temperature of the filament?

a. 30100 K

b. 378 K

c. 1627 K

d. 814 K

e. 1162 K

+4

Answers (1)

Know the Answer?

Lillian Gallegos · Answer 1

162.8 K

Explanation:

initial current = io

final current, i = io/8

Let the potential difference is V.

coefficient of resistivity, α = 43 x 10^-3 / K

Let the resistance is R and the final resistance is Ro.

The resistance varies with temperature

R = Ro (1 + α ΔT)

V/i = V/io (1 + α ΔT)

8 = 1 + 43 x 10^-3 x ΔT

7 = 43 x 10^-3 x ΔT

ΔT = 162.8 K

Thus, the rise in temperature is 162.8 K.