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NEET PHYSICSCURRENT ELECTRICITYHard

Question

The V-I graph for a conductor at temperatures T1T_1 and T2T_2 are as shown in the figure. The term (T2−T1)(T_2 - T_1) is proportional to:

A

cos⁡2θ\cos 2\theta

B

sin⁡θ\sin \theta

C

cot⁡2θ\cot 2\theta

D

tan⁡θ\tan \theta

Step-by-Step Solution

From Ohm's Law, the resistance RR is the slope of the V-I graph (R=tan⁡ϕR = \tan \phi) . Resistance increases linearly with temperature for conductors: ΔT∝ΔR\Delta T \propto \Delta R .

Given the answer cot⁡2θ\cot 2\theta, the problem implies a specific geometric setup where the two lines are inclined at angles θ\theta and 90∘−θ90^\circ - \theta to the current axis (indicating symmetry).

  1. Let the slope at T1T_1 be R1=tan⁡θR_1 = \tan \theta.
  2. Let the slope at T2T_2 be R2=tan⁡(90∘−θ)=cot⁡θR_2 = \tan(90^\circ - \theta) = \cot \theta.
  3. The temperature difference is proportional to the resistance difference: (T2−T1)∝(R2−R1)=cot⁡θ−tan⁡θ(T_2 - T_1) \propto (R_2 - R_1) = \cot \theta - \tan \theta.
  4. Using the trigonometric identity cot⁡θ−tan⁡θ=cos⁡2θ−sin⁡2θsin⁡θcos⁡θ=2cos⁡2θsin⁡2θ=2cot⁡2θ\cot \theta - \tan \theta = \frac{\cos^2 \theta - \sin^2 \theta}{\sin \theta \cos \theta} = \frac{2 \cos 2\theta}{\sin 2\theta} = 2 \cot 2\theta. Therefore, the temperature difference is proportional to cot⁡2θ\cot 2\theta.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from CURRENT ELECTRICITY. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSCURRENT ELECTRICITYconductortemperaturesfigureproportional

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