Hey guys I need some insight to this calculus problem.
The resistance R of a copper wire at temperature T = 30° C is R = 15 Ω. Estimate the resistance at
T = 37° C, assuming that dR/dT at T = 30 is 0.13 Ω/(° C). (Round your answer to two decimal places.)

I know that I need first to come up with a base model to then find the differential. However....I have no idea what formula to use other than V=IR. Something tells me that I need to incorporate the T value somewhere but I'm at a loss. Please help. Thanks

Question

Hey guys I need some insight to this calculus problem. 
The resistance R of a copper wire at temperature T = 30° C is R = 15 Ω. Estimate the resistance at 
T = 37° C, assuming that dR/dT at T = 30 is 0.13 Ω/(° C). (Round your answer to two decimal places.)

I know that I need first to come up with a base model to then find the differential. However....I have no idea what formula to use other than V=IR. Something tells me that I need to incorporate the T value somewhere but I'm at a loss. Please help. Thanks <3

oswaldmurphy · Answer

Welcome to openstudy! @TheSmartOne should know this one :D

dumbcow · Answer

Let dR/dT be the slope, assume a linear function for R
$$R = \frac{dR}{dT} (T - T_0) + R_0$$
plug in initial values
$$R = 0.13(37-30) + 15$$
$$R = 15.91$$

varaujo19 · Answer

Thank you so much @dumbcow