A heating element made of tungsten wire is connected to a large battery that has

Question

A heating element made of tungsten wire is connected to a large battery that has negligible internal resistance. When the heating element reaches 80.0C, it consumes electrical energy at a rate of 420 W . Assume that the temperature coefficient of resistivity has the value given in Table 25.2 in the textbook and that it is constant over the temperature range in this problem. In the equation R(T)=R0[1+(TT0)] take T0 to be 20.0C.

What is its power consumption when the temperature of the heating element is 150.0 C ?

Explanation / Answer

Here,

for tungestun

a = 0.0045 1/degree C

let the resistance at 20 degree is Ro

now , at 80 degree C

R1 = Ro * (1 + (80 - 20) * 0.0045)

R1 = 1.27 * Ro

at 150 degree C

R2 = Ro * (1 + (150- 20) * 0.0045)

R2 = 1.585 * Ro

as power is given as

Power = V^2/R

for same potential

P2/P1 = R1/R2

P2/420 = 1.27 * Ro/( 1.585 * Ro)

P2 = 1.27 * 420/1.585

P2 = 336.5 W

the power consumed at 150 degree C is 336.5 degree C

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