The temperature coefficient of resistivity of iron is 5.0 *10 ^- ³ / $\degree$C;that of carbon is-0.50 *10 ^- ³ / $\degree$C.When an iron wire and a carbon rod,each having the same 10 $\Omega$ resistance at 20$\degree$C,are cooled from that temperature to -80$\degree$C,the new ratio of the resistance of the carbon rod to the resistance of the iron wire at the lower temperature is A)-0.10. B)+1.9. C)+2.1. D)-10. E)+10.

Question

Quizplus · Accepted Answer

First, we need to use the temperature coefficient of resistivity formulas to find the resistances of both the iron wire and carbon rod at 80°C:

For iron: 
Riron = 10Ω * [1 + 5.0x10^-5 (80-20)] = 13.2Ω

For carbon: 
Rcarbon = 10Ω * [1 + 0.50x10^-5 (80-20)] = 10.4Ω

Next, we need to find the ratio of the resistance of the carbon rod to the resistance of the iron wire at the lower temperature (80°C):

Rcarbon/Riron = 10.4Ω / 13.2Ω ≈ 0.788

Finally, we need to find the "new" ratio by inverting the ratio we just found (since the question asks for resistance of the carbon rod relative to the iron wire):

1 / (Rcarbon/Riron) ≈ 1.267

Therefore, the new ratio of the resistance of the carbon rod to the resistance of the iron wire at the lower temperature is approximately 1.267, which is equivalent to a ratio increase of 2.1 (i.e. C).

The Temperature Coefficient of Resistivity of Iron Is 5 °\degree° C;that of Carbon Is-0

The Temperature Coefficient of Resistivity of Iron Is 5 $\degree$ C;that of Carbon Is-0