Question

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

Answer 1

ΔT = 1628 K

Step-by-step explanation:

Let '
`i_o`' be initial current

then, final current= i =
`i_o`/8

Let V represents potential difference.

coefficient of resistivity, α = 4.3 x
`10^-^3` /K

The resistance varies with temperature

R = Ro ( 1 + α ΔT)

where,

R is resistance and
`R_o` is the final resistance

V/i = V/
`i_o`(1 + α ΔT )

8 = 1 + (4.3 x
`10^-^3` x ΔT )

7 = 4.3 x
`10^-^3`x ΔT

ΔT = 1628 K

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