V- I graph for a metallic wire at two different temperature `T_(1)` and `T_(2)` is shown in figure. Which of the two temperature is higher and why?

Options

A. `cos 2 theta`
B. `sin 2 theta`
C. `cot 2 theta`
D. `tan 2 theta`

Answer

C

Explanation

`R_(1) = tan theta = R_(0) ( 1+ alpha T_(1))`
and`R_(2) = cos theta = R_(0) ( 1+ alpha T_(2))`
`:. cot theta - tan theta= = R_(0) ( 1+ alpha T_(2))- R_(0) ( 1+ alpha T_(2)) `
`R_(0)alpha (T_(2) - T_(1))`
or `T_(2) - T_(1) = (1)/(alpha R_(0)) (cot theta - tan theta)`
`(1)/(alpha R_(0)) ((cot theta)/(sin theta) -(sin theta)/(cos theta))= (2 cos 2 theta)/(alpha R_(0) sin 2 theta)`
`= (2)/(alpha R_(0)) cot 2 theta or T_(1) - T_(2) prop cot 2 theta`