When the tungsten filament in a 60 W, 120 V light bulb reaches 2010° C, 60 W of

Question

When the tungsten filament in a 60 W, 120 V light bulb reaches 2010° C, 60 W of electric power is used to produce light and heat.

(a) Find the current through the filament under these conditions, which are established very shortly after the light is turned on.

(b) Find the filament current when the light is first turned on, assuming an initial filament temperature of 20° C. Find the power used when the light is first turned on, assuming an initial filament temperature of 20° C.

(c) Estimate the time needed to heat the filament to 2010° C. The filament has a mass of 0.037 g and a specific heat of 0.032 cal/g-C°.

Please explain and show formulas used! Thank you!

Explanation / Answer

Given that

When the tungsten filament in a 60 W, 120 V light bulb reaches 2010° C, 60 W of electric power is used to produce light and heat.

We know that Power =V2/R

Then the resisitance (R) =V2/P

From this we can write

R =Ro(1+0.0045(2010-20)

120*120/60=Ro(1+0.0045(2010-20)

Ro =240/9.955=24.108ohms

a)

The current through the filament is given by

i =V/R =120/24.108=4.977A

b)

The power used when the light is first turned on, assuming an initial filament temperature of 20° C is given by

P =V*I =120*4.977A =597.312W

c)

The time needed to heat the filament (t) =Q/P =mCDeltT/P =(0.037)(0.032)(2010-20)/60=0.0392s

.

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