Before bendable tungsten filaments were developed, Thomas Edison used carbon fil

Question

Before bendable tungsten filaments were developed, Thomas Edison used carbon filaments in his light bulbs. Though carbon has a very high melting temperature (3599 °C), its sublimation rate is high at high temperatures. So carbon-filament bulbs were kept at lower temperatures, thereby rendering them dimmer than later tungsten-based bulbs. A typical carbon-filament bulb requires an average power of 40 W, when 110 volts is applied across it, and has a filament temperature of 1800 °C. Carbon, unlike copper, has a negative temperature coefficient of resistivity:
a = -0.0005 °C-1.
Calculate the resistance at room temperature (20 °C) of this carbon filament. (When entering units, use ohm for O.)

Explanation / Answer

Power = Voltage^2/Resistance V= 110 R(1800) =? 40 = 110^2/R => R(1800)= 302.5 now using the equation of resistance and temp we have R(1800) = R(20)(1 + a(change in temp )) R(1800) = R(20)(1 -0.0005*1780) => R(20) = R(1800)/(1 - .89) => R(20) = 16363.6364O

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