This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1: The temperature dependence of resistance is usually given as \(\mathrm{R}=\mathrm{R}_{\mathrm{o}}(1+\alpha \Delta \mathrm{t})\). The resistance of a wire changes from \(100 \Omega\) to \(150 \Omega\) when its temperature is increased from \(27^{\circ} \mathrm{C}\) to \(227^{\circ} \mathrm{C}\). This implies that \(\alpha=2.5 \times 10^{-3} /{ }^{\circ} \mathrm{C}\). Statement 2: \(R=R_{i}(1+\alpha \Delta T)\) is valid only when the change in the temperature \(\Delta T\) is small and \(\Delta R= \left(\mathrm{R}-\mathrm{R}_{\mathrm{o}}\right) \ll \mathrm{R}_{\mathrm{o}}\).

(A) Statement-1 is true, Statement-2 is false

(B) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.

(C) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.

(D) Statement-1 is false, Statement-2 is true

JEE Main · 2009 · 12 Apr 2009 · Offline · Current Electricity

This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement-1: The temperature dependence of resistance is usually given as

R = R_{o} (1 + α Δ t)

. The resistance of a wire changes from

100Ω

150Ω

when its temperature is increased from

2 7^{\circ} C

22 7^{\circ} C

. This implies that

α = 2.5 \times 1 0^{- 3} /^{\circ} C

.
Statement 2:

R = R_{i} (1 + α Δ T)

is valid only when the change in the temperature

Δ T

is small and

Δ R = (R - R_{o}) ≪ R_{o}

(A)Statement-1 is true, Statement-2 is false✓ Correct
(B)Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.
(C)Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.
(D)Statement-1 is false, Statement-2 is true

Answer: (A)

Solution

Putting the numbers into

R = R_{0} (1 + α Δ t)

with

R_{0} = 100 Ω

R = 150 Ω

and

Δ t = 20 0^{\circ}

C gives

150 = 100 (1 + 200 α)

, so

α = 2.5 \times 1 0^{- 3}^{\circ} C^{- 1}

, which makes the first statement true. The second statement claims the linear law is valid only for small temperature changes with

Δ R ≪ R_{0}

, yet here

Δ T = 20 0^{\circ}

C is large and

Δ R = 50 Ω

is half of

R_{0}

, and the formula was still applied, so that restrictive claim is false.

JEE Main · 2009 · 12 Apr 2009 · Offline · Single correct option

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JEE Main · 2009 · 12 Apr 2009 · Offline · Current Electricity

Solution

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