AP EAMCET Engineering 18 Sep 2020 Shift 2 Paper

V−I graph for conductor at temperature T1 and T2 is shown in the figure.We know that resistance of a conductor is directly proportional to its temperature.
Hence, R1∝T1⇒tan‌θ∝T1
⇒‌‌tan‌θ=KT1.....(i)
and ‌‌R2∝T2
⇒‌‌tan(90∘−θ)∝T2
⇒‌‌cot‌θ∝T2
⇒‌‌cot‌θ=KT2 ....(ii)
∴ From Eqs. (i) and (ii), we get
KT2−KT1=cot‌θ−tan‌θ
K(T2−T1)=‌

cos‌θ

sin‌θ

−‌

sin‌θ

cos‌θ

⇒‌‌T2−T1=‌

cos2θ−sin2θ

K‌sin‌θ‌cos‌θ

⇒‌‌T2−T1∝cot‌2‌θ