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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 wire has a resistance of \( 24 \, \Omega \) at \( 25^\circ \text{C} \) and \( 25.8 \, \Omega \) at \( 75^\circ \text{C

**Resistivity** depends on material and temperature, not geometry. For metallic conductor, ρ ≈10⁻⁸ Ω·m for copper. Given ρ=4×10⁻⁸ Ω·m, l=2 m, A=π r², R calculation uses R=ρ l/A. Stretching wire conserves volume V = l A = l' A', so A' = A l/l', new R' = ρ l'²/V. Use: R_t = R₀ [1 + α (T - T₀)] . Substitute: 25.8 = 24 [1 + α (75 - 25)] . Solve: 25.8 = 24 + 1200α ⇒ 1200α = 1.8 ⇒ α = (1.8/1200) = 1.5 × 10⁻³ °C⁻¹ . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT],

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

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