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  • The V-I graph for a conductor at temperatures T1 and T2 are as shown in the figure, (T2 - T1) is proportional to <img alt="" src="https://cdn.entrance360.com/media/uploads/2023/07/08/4.png"

The V-I graph for a conductor at temperatures T1 and T2 are as shown in the figure, (T2 - T1) is proportional to

Option: 1

\mathrm{\cos 2 \theta}


Option: 2

\mathrm{\sin 2 \theta}


Option: 3

\mathrm{\cot 2 \theta}


Option: 4

\tan 2 \theta


Answers (1)

best_answer

According to Ohm's law
\mathrm{V}=\mathrm{Ri}
or \mathrm{\mathrm{R}=\frac{\mathrm{V}}{\mathrm{i}}=\tan \theta}

\mathrm{Hence, \mathrm{R}_1=\tan \theta}
\mathrm{\mathrm{R}_2=\tan (90-\theta)=\cot \theta}
\mathrm{As\: \mathrm{R} \propto temperature}

\mathrm{\mathrm{R}_1 \propto \mathrm{T}_1 ; \text { and } \mathrm{R}_2 \propto \mathrm{T}_2}
\mathrm{\mathrm{~T}_2-\mathrm{T}_1 \propto \cot \theta-\tan \theta}
\mathrm{ \mathrm{T}_2-\mathrm{T}_1 \propto \frac{\cos ^2 \theta-\sin ^2 \theta}{\sin \theta \cdot \cos \theta}}
\mathrm{ \text { or } \mathrm{T}_2-\mathrm{T}_1 \propto \mathrm{x} \cot 2 \theta}
\mathrm{ \therefore(\mathrm{C})}

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