#nichrome

Temperature Dependence of Resistance and Resistivity

A nichrome wire has a resistance of \( 80 \, \Omega \) at \( 25^\circ \text{C} \) and \( \alpha = 1.7 \times 10^{-4} \,

**Temperature dependence** of resistance R_t = R₀[1+α(T-T₀)], α temperature coefficient (per °C), R₀ resistance at T₀ (Ω). For metals α positive ≈10⁻³ /°C, resistance increases with temperature because τ decreases due to increased phonon scattering, n nearly constant. Use: R_t = R₀ [1 + α (T - T₀)] . Substitute: R_t = 80 [1 + 1.7 × 10⁻⁴ (225 - 25)] . Calculate: R_t = 80 [1 + 1.7 × 10⁻⁴ × 200] = 80 [1 + 0.034] = 80 × 1.034 = 82.72 Ω . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT], Kirchhoff's ΣI=0, ΣV=0, R_eq series/parallel,

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Temperature Dependence of Resistance and Resistivity

A nichrome wire has a resistance of \( 50 \, \Omega \) at \( 20^\circ \text{C} \) and \( \alpha = 1.7 \times 10^{-4} \,

**Conductivity** σ=1/ρ decreases with temperature for metals, σ = n e² τ/m, τ ∝1/T due to lattice vibrations. For semiconductors, n increases exponentially with T, so σ increases, opposite to metals, explaining why metallic resistance rises with temperature. Use: R_t = R₀ [1 + α (T - T₀)] . Substitute: R_t = 50 [1 + 1.7 × 10⁻⁴ (380 - 20)] . Calculate: R_t = 50 [1 + 1.7 × 10⁻⁴ × 360] = 50 [1 + 0.0612] = 50 × 1.0612 = 53.06 Ω . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT], Kirchhoff's ΣI=0, ΣV=0, R_eq series/parallel,

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Resistance, Resistivity and Ohm's Law

A nichrome wire has a resistance of \( 60 \, \Omega \) at \( 25^\circ \text{C} \) and \( \alpha = 1.7 \times 10^{-4} \,

**Ohm's law deviation** at high fields occurs when τ or n vary with E, resistivity ρ = m/(n e² τ) changes, non-ohmic behaviour seen in semiconductors, electrolytes. At moderate fields, linear V-I holds, slope = R. Use: R_t = R₀ [1 + α (T - T₀)] . Substitute: R_t = 60 [1 + 1.7 × 10⁻⁴ (225 - 25)] . Calculate: R_t = 60 [1 + 1.7 × 10⁻⁴ × 200] = 60 [1 + 0.034] = 60 × 1.034 = 62.04 Ω . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT], Kirchhoff's ΣI=0, ΣV=0, R_eq series/parallel, V =

Ref: NCERT > Physics Book > Current Electricity > Resistance, Resistivity and Ohm's Law

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Resistance, Resistivity and Ohm's Law

A nichrome wire has a resistance of \( 80 \, \Omega \) at \( 20^\circ \text{C} \) and \( \alpha = 1.7 \times 10^{-4} \,

**Resistance** R = ρ l/A, ρ resistivity (Ω·m), l length (m), A area (m²), ρ = m/(n e² τ) from Drude model, τ average collision time. Ohm's law V = I R holds when ρ constant, independent of V. Volume constant stretching l→2l implies A→A/2, so R' = ρ·2l/(A/2)=4R, resistance quadruples when length doubles at constant volume. Use: R_t = R₀ [1 + α (T - T₀)] . Substitute: R_t = 80 [1 + 1.7 × 10⁻⁴ (300 - 20)] . Calculate: R_t = 80 [1 + 1.7 × 10⁻⁴ × 280] = 80 [1 + 0.0476] = 80 × 1.0476 ≈ 83.81 Ω .

Ref: NCERT > Physics Book > Current Electricity > Resistance, Resistivity and Ohm's Law

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Resistance, Resistivity and Ohm's Law

A nichrome wire has a resistance of \( 60 \, \Omega \) at \( 30^\circ \text{C} \) and \( \alpha = 1.7 \times 10^{-4} \,

**Resistance** R = ρ l/A, ρ resistivity (Ω·m), l length (m), A area (m²), ρ = m/(n e² τ) from Drude model, τ average collision time. Ohm's law V = I R holds when ρ constant, independent of V. Volume constant stretching l→2l implies A→A/2, so R' = ρ·2l/(A/2)=4R, resistance quadruples when length doubles at constant volume. Use: R_t = R₀ [1 + α (T - T₀)] . Substitute: R_t = 60 [1 + 1.7 × 10⁻⁴ (330 - 30)] . Calculate: R_t = 60 [1 + 1.7 × 10⁻⁴ × 300] = 60 [1 + 0.051] = 60 × 1.051 = 63.06 Ω .

Ref: NCERT > Physics Book > Current Electricity > Resistance, Resistivity and Ohm's Law

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