The resistance of a conductor is 5 ohm at 50*c and 6 ohm at 100*c.Its resistance at 0*is??THANK YOU!!

Question

Olivia Askew · Accepted Answer

Well, try thinking about it this way: the resistance changed by only #1 Omega# over #50^oC#, which is a pretty large temperature range. So, I would say it's safe to assume the change in resistance with respect to temperature (#(DeltaOmega)/(DeltaT)#) is pretty much linear. #(DeltaOmega)/(DeltaT) ~~ (1 Omega)/(50^oC)# #DeltaOmega = (1 Omega)/(100^oC-50^oC)*(0^oC-50^oC) ~~ -1 Omega# #Omega_(0^oC) ~~ 4 Omega#

Julia Aguilar · Answer

Its resistance at #0^@"C""# is 4 ohm.

#R_T=(1+alpha T)R#, where #R_T=#Resistance at any temperature, #alpha#=constant of material, #R=#resistance at Zero degree Celsius. At 50°C: #R_50=(1+50alpha )R#=#"5 ohm"# #" "color(blue)((1))# At 100 °C: #R_100=(1+100alpha)R = "6 ohm"# #" "color(blue)((2))# At 0°C: #R_0=(1+0)R# #R_0=R# #" "color(blue)((3))# Determination R from equations #color(blue)((1))# and #color(blue)((2))#** by #color(blue)((1))/color(blue)((2)) => (1+50alpha)/(1+100alpha) =5/6# #6 + 300alpha = 5 + 500alpha => alpha = 1/200# Use this value in equation #color(blue)((1))# #(1+ 1/200 * 50) * R = 5 => 5/4* R = 5 => R = "4 ohm"# According to equation #color(blue)((3))#, you have #R_0 = R = "4 ohm"# Therefore, its resistance at #0^@"C"# is #"4 ohm"#.

Julia Aguilar · Answer

undefined The resistance of the conductor at 0°C is 4 ohms.