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## Homework Statement

When an incandescent light bulb is switched on, it can take a few moments for the filament to fully heat up and reach its equilibrium temperature. Assume the filament of a given light bulb is made of Tungsten, and also

assume the potential difference across the filament is maintained at a constant value during this short warm up

period. If the ‘steady state’ current is measured to be only 1/6 of the current drawn when the lamp is first turned on, then what is the final operating temperature of the filament? Assume the initial temperature of the filament is 20 °C, and assume the resistivity increases linearly with increasing temperature.

## Homework Equations

R = R

_{o}[1+∝(T-T

_{o})]

## The Attempt at a Solution

So im not given the resistance here but i am told the voltage is constant throughout this warm up. So i can use

R = V/I

Plug into R = R

_{o}[1+∝(T-T

_{o})]

V/I = V/I

_{o}[1+∝(T-T

_{o})]

Since voltage is constant i can divide both sides to cancel them out, also multiply both sides by I and I

_{o}leaving me with

I

_{o}= I [1+∝(T-T

_{o})]

Im told the steady state current is only 1/6 of the initial current when the bulb is first turned on so i can say

I= 1/6 I

_{o}and plug it into the equation.

I

_{o}= 1/6 I

_{o}[1+∝(T-T

_{o})]

From here i cancel out I

_{o}from both sides and solve for T. The answer is get is

1131

^{o}C, is this correct?