The V-l graph for a conductor at temperatures `T_(1) " and " T_(2)` are as shown in the figure. The term `T_(2) -T_(1)` is proportional to

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+alphaT_(1))`
and `R_(2)=cost theta =R_(0)(1+alphaT_(2))`
`cot theta-tan theta=R_(0)(1+alpha T_(2))-R_(0)(1+alphaT_(1))=R_(0)alpha(T_(2)-T_(1))`
or `T_(2)-T_(1)=(1)/(alphaR_(0))(cot theta- tan theta)`
`=(1)/(alpha R_(0)) (cot theta - tan theta)`
`=(1)/(alpha R_(0))((cos theta)/(sin theta)-(sin theta)/(cos theta))`
`=(2 cos 2 theta)/(alpha R_(0) sin theta)=(2 cos 2theta)/(alpha R_(0) sin 2 theta)`
`implies " " =(2)/(alpha R_(0))cot 2 theta`