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#electrical properties

12 public questions tagged with this topic.

Semiconductors, Types and Energy Bands

Which of the following materials has the highest resistivity?

**Semiconductor properties** distinguish from conductors and insulators by temperature dependence and doping response. At 0 K intrinsic acts as insulator, conductivity due to thermally generated electron-hole pairs, number of outer electrons 4 for Si/Ge forming covalent bonds, each atom shares electrons, crystal with N atoms has 4N valence electrons, 2N bonds. Resistivity ( rho ) distinguishes materials: metals have low resistivity ( 10⁻² to 10⁻⁸ Ω m ), semiconductors intermediate ( 10⁻⁵ to 10⁶ Ω m ), and insulators high ( 10¹⁰ to 10¹⁹ Ω m ). Among the options, insulators have the highest resi

Ref: NCERT > Physics Book > Electronic Devices > Semiconductors, Types and Energy Bands

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Semiconductors, Types and Energy Bands

The resistivity of insulators is typically in the range:

**Types of semiconductors** elemental Si, Ge group IV with 4 valence electrons, compound GaAs, InP etc. Intrinsic has n_e = n_h, extrinsic doped with pentavalent donors (P, As) gives n-type excess electrons, trivalent acceptors (B, Al) gives p-type excess holes, resistivity range semiconductors 10⁻⁵ to 10⁶ Ω·m vs insulators 10¹¹ Ω·m. Insulators have high resistivity ( 10¹⁰ to 10¹⁹ Ω m ) or low conductivity ( 10⁻¹¹ to 10⁻¹⁹ S m⁻¹ ), preventing significant current flow. Substituting values gives 10¹⁰ to 10¹⁹ Ω m, which matches expected behaviour for this semiconductor device configuration, confi

Ref: NCERT > Physics Book > Electronic Devices > Semiconductors, Types and Energy Bands

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Potentiometer, Conductivity and Special Cases

A conductor has a resistivity of \( 8 \times 10^{-8} \, \Omega \text{m} \) and \( \alpha = 4 \times 10^{-3} \, ^\circ\te

**Potentiometer** measures potential difference without drawing current, using null deflection, principle V ∝ l, l balance length, accurate because no I r drop. Potential drop across resistor V = I R arises because electric field does work on charges, energy converted to heat, maintaining E = -dV/dx along wire. Use: rho_t = rho₀ [1 + α (T - T₀)] . Substitute: rho_t = 8 × 10⁻⁸ [1 + 4 × 10⁻³ (70 - 20)] . Calculate: rho_t = 8 × 10⁻⁸ [1 + 0.2] = 8 × 10⁻⁸ × 1.2 = 9.6 × 10⁻⁸ Ω m . Applying I = n e A v_d, R

Ref: NCERT > Physics Book > Current Electricity > Potentiometer, Conductivity and Special Cases

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Potentiometer, Conductivity and Special Cases

A conductor has a resistivity of \( 5 \times 10^{-8} \, \Omega \text{m} \) and \( \alpha = 4 \times 10^{-3} \, ^\circ\te

**Potentiometer** measures potential difference without drawing current, using null deflection, principle V ∝ l, l balance length, accurate because no I r drop. Potential drop across resistor V = I R arises because electric field does work on charges, energy converted to heat, maintaining E = -dV/dx along wire. Use: rho_t = rho₀ [1 + α (T - T₀)] . Substitute: rho_t = 5 × 10⁻⁸ [1 + 4 × 10⁻³ (100 - 30)] . Calculate: rho_t = 5 × 10⁻⁸ [1 + 0.28] = 5 × 10⁻⁸ × 1.28 = 6.4 × 10⁻⁸ Ω m . Applying I = n e A v_d, R

Ref: NCERT > Physics Book > Current Electricity > Potentiometer, Conductivity and Special Cases

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Potentiometer, Conductivity and Special Cases

A wire of length \( 8 \, \text{m} \) and cross-sectional area \( 2 \times 10^{-6} \, \text{m}^2 \) has a resistance of \

**Potential difference drop** across resistor when current flows because charges lose potential energy qV = I² R t as heat, field E = V/l drives drift, maintaining current. At very high E, velocity saturation or heating changes τ, causing non-ohmic behaviour. Resistance: R = (rho l/A) . Rearrange: rho = (R A/l) . Substitute: rho = (16 × 2 × 10⁻⁶/8) = 4 × 10⁻⁶ Ω m . 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 = ε - I r and P = I²R, evaluation yields 4.0 × 10⁻⁶ Ω m, consistent

Ref: NCERT > Physics Book > Current Electricity > Potentiometer, Conductivity and Special Cases

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Wheatstone Bridge and Meter Bridge

Why does the resistance of a conductor increase when its cross-sectional area is reduced?

**Wheatstone bridge balance** condition R₁/R₂ = R₃/R₄, R₄ = R₂ R₃/R₁, when galvanometer current zero, potentials at midpoints equal. At balance, no current through galvanometer, enabling precise resistance measurement independent of source voltage. Resistance R = rho l / A . Reducing A increases R inversely, as fewer charge carriers can pass through a smaller area, increasing opposition to current flow. 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 = ε - I r and P = I²R, evaluation yields Fewer paths for current,

Ref: NCERT > Physics Book > Current Electricity > Wheatstone Bridge and Meter Bridge

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Temperature Dependence of Resistance and Resistivity

Why does the resistance of a conductor increase when it is stretched to double its length, assuming volume remains const

**Resistivity temperature variation** ρ_t = ρ₀[1+α(T-T₀)], α ≈4×10⁻³ /°C for copper, 1.7×10⁻⁴ /°C for nichrome. Given R=60 Ω at 30°C, α=1.7×10⁻⁴ /°C, T=330°C, ΔT=300°C, R_t=60[1+1.7×10⁻⁴×300]=60×1.051=63.06 Ω, modest increase for nichrome due to small α. Resistance R = rho l / A . Doubling length ( l' = 2l ) halves area ( A' = A/2 ) due to constant volume. Thus, R' = rho (2l) / (A/2) = 4 rho l / A = 4R , due to both increased length and decreased cross-sectional area. 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 > Temperature Dependence of Resistance and Resistivity

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Resistance, Resistivity and Ohm's Law

A wire of length \( 5 \, \text{m} \) and resistance \( 20 \, \Omega \) is stretched to \( 10 \, \text{m} \). What is the

**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. Volume constant: l A = l' A' ⇒ A' = (A/2) . New resistance: R' = (rho l'/A') = (rho (2l)/(A/2)) = 4 (rho l/A) = 4R = 4 × 20 = 80 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 = ε - I r and P = I²R, evaluation yields 80 Ω, consistent

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

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Temperature Dependence of Resistance and Resistivity

In a metallic conductor, if the temperature increases significantly, what happens to the conductivity of the material?

**Resistivity temperature variation** ρ_t = ρ₀[1+α(T-T₀)], α ≈4×10⁻³ /°C for copper, 1.7×10⁻⁴ /°C for nichrome. Given R=60 Ω at 30°C, α=1.7×10⁻⁴ /°C, T=330°C, ΔT=300°C, R_t=60[1+1.7×10⁻⁴×300]=60×1.051=63.06 Ω, modest increase for nichrome due to small α. Conductivity ( sigma = 1 / rho ) is inversely proportional to resistivity ( rho = m / (n e² tau) ). As temperature increases, the relaxation time ( tau ) decreases due to more frequent collisions, increasing rho and thus decreasing sigma . 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 = ε -

Ref: NCERT > Physics Book > Current Electricity > Temperature Dependence of Resistance and Resistivity

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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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PHYSICS

The resistivity of insulators is typically in the range:

Insulators have high resistivity ( 10¹⁰ to 10¹⁹Ω m ) or low conductivity ( 10⁻¹¹ to 10⁻¹⁹ S m^{-1 ), preventing significant current flow. This follows from NCERT principle where the relation explains the outcome clearly for students in simple steps.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Current Electricity, Topic: Resistivity, temperature dependence and circuit analysis.

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