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

2 Answers
May 30, 2015

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

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

Explanation:

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 degrees Celsius:

R_50=(1+50alpha )R="5 ohm" " "color(blue)((1))

At 100 degrees Celsius:

R_100=(1+100alpha)R = "6 ohm" " "color(blue)((2))

At zero degrees Celsius:

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".