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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 4.3 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

Respuesta :

Rau7star

Answer:

ΔT = 1628 K

Explanation:

Let '[tex]i_o[/tex]' be initial current

then, final current= i = [tex]i_o[/tex]/8

Let V represents potential difference.

coefficient of resistivity, α = 4.3 x [tex]10^-^3[/tex] /K

The resistance varies with temperature

R = Ro ( 1 + α ΔT)

where,

R is resistance and [tex]R_o[/tex] is  the final resistance

V/i = V/ [tex]i_o[/tex](1 + α ΔT )

8 = 1 + (4.3 x [tex]10^-^3[/tex] x ΔT )

7 = 4.3 x [tex]10^-^3[/tex]x ΔT

ΔT = 1628 K

Therefore, the change in temperature of the filament is  1628 K