Question

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

Answer 1

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`

Answer 2

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"`.