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

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.

the working equation for the angular size is the product of the physical size and 360 degrees divided by the product of two pi and distance from earth. the minimum size would be 0.559 degrees while the maximum size would be 0.49 degrees.