TS EAMCET · Physics · Current Electricity

The resistance of a wire is \(2.5 \Omega\) at a temperature 373 K . If the temperature coefficient of resistance of the material of the wire is \(3.6 \times 10^{-3} \mathrm{~K}^{-1}\), its resistance at a temperature 273 K is nearly

A \(1.84 \Omega\)
B \(2.46 \Omega\)
C \(0.82 \Omega\)
D \(4.58 \Omega\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(1.84 \Omega\)

Step-by-step Solution

Detailed explanation

For a wire, \(\mathrm{R}_1=2.5 \Omega, \mathrm{~T}_1=373 \mathrm{k}, \alpha=3.6 \times 10^{-3} \mathrm{~K}^{-2}, \mathrm{~T}_2=273 \mathrm{~K}\) \(\therefore\) Resistance, \(\mathrm{R}_2=\mathrm{R}_1(\mathfrak{j}+\alpha \Delta \mathrm{T})\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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List - I			List - II
A	Gravitational potential	I	$M^{0} L^{2} T^{- 2} K^{- 1}$
B	Stefan's constant	II	$M^{0} L^{2} T^{- 2}$
C	Permittivity	III	${ML}^{0} T^{- 3} K^{- 4}$
D	Specific heat capacity	IV	$M^{- 1} L^{- 3} T^{4} I^{2}$