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

Options

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

Answer

C

Explanation

For conductors, resistance ∝ temperature
i.e., `R prop T`
`R_(1) = tan theta_(1)` and `R_(2) = tan (90 - theta) prop T_(2)`
`rArr tan theta_(1) = kT_(1)` and `cot theta = kT_(2)`
Now, `k(T_(2)-T_(1)) prop T_(1)` and `R_(2) = tan (90- theta) prop T_(2)`
Now
`k(T_(2)-T_(1)) = cot theta - tan theta =((cos theta)/(sin theta) - (sin theta)/(cos theta))`
`therefore (T_(2)-T_(1)) prop cot 2theta`