(i) Define the 'temperature coefficient of resistance' of a metal. (ii) Show the variation of the resistivity of copper with a rise in temperature. (iii) The resistance of a wire is $10\,\Omega$ at $27^\circ\text{C}$. Find its resistance at $-3^\circ\text{C}$, given the temperature coefficient of resistance $\alpha=1.70\times10^{-4}\,^\circ\text{C}^{-1}$.

(i) The fractional change in resistance per degree rise in temperature, $\alpha=\dfrac{1}{R_0}\dfrac{\Delta R}{\Delta T}$. (ii) The resistivity of copper rises (approximately parabolically) with temperature. (iii) $R\approx9.95\,\Omega$.

CBSE Class 12 · 2024 · Current ElectricityShort Answer

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(i) Define the 'temperature coefficient of resistance' of a metal.
(ii) Show the variation of the resistivity of copper with a rise in temperature.
(iii) The resistance of a wire is

10 Ω

2 7^{\circ} C

. Find its resistance at

- 3^{\circ} C

, given the temperature coefficient of resistance

α = 1.70 \times 1 0^{- 4}^{\circ} C^{- 1}

Solution

(i)

α = \frac{R - R _{0}}{R _{0} Δ T}

— the change in resistance per unit resistance per degree rise. (ii) For copper

ρ

increases with

T

(nearly linearly over normal ranges, curving at low

T

). (iii)

R = R_{27} [1 + α (T - 27)] = 10 [1 + 1.70 \times 1 0^{- 4} (- 3 - 27)] = 10 [1 - 1.70 \times 1 0^{- 4} \times 30] = 10 (1 - 0.0051) = 9.95 Ω.

CBSE Class 12 Board · 2024 · Subjective

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