ent Gradebook ORION Downloadable eTextbook ent FULL SCREEN PRINTER VERSTON BACK

Question

ent Gradebook ORION Downloadable eTextbook ent FULL SCREEN PRINTER VERSTON BACK pter 26, Problem 021 A common fashlight bulb ls rated at 0.31 A and 3.0 V (the values of the current and voltage under operating conditions). If the resistance of the bulb flament at room what is the temperature of the f lament when the bulb is on? The temperature coefficient of resistivity is 3.8 20°C temperature material. is 1.3 10 3 K i for the filament Number Units the tolerance is +/-2% Question Attempts: 0 of 10 used SAVE FOR LATER SUBMIT ANSWER

Explanation / Answer

Let V(3.0V) and I(0.31A) be the normal operating voltage and current of the bulb.

Under normal operating conditions, R = V/I = 3.0/0.31 = 9.68 Ohms

Given that at 20°C (293K), R0 = 1.3 ohms and TCR = 3.8 x 10^-3 1/K

The definition of TCR is, TCR = (1/R)*dR/dT -> TCR*dT = (1/R)*dR

Integrate it with respect to dT with limits (T0 = 20°C to T) and (R0 = 1.3 ohms to R), we have

TCR*(T -T0) = Ln(R/R0)

T - 293 = Ln(9.68/1.3) * 1/3.8 x 10^-3

T = 528 + 293 = 821.3K (or 548.19°C)

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