JEE/NEET Physics · Current Electricity series · Part 2 of 8 · All parts →
- Ohm’s law: V = IR for ohmic conductors at constant temperature — ratio V/I stays fixed
- Resistance R = ρL/A — longer wire, more resistance; fatter wire, less
- Resistivity ρ is the MATERIAL’s property: copper 1.7×10⁻⁸, rubber ~10¹³ Ω·m
- Conductivity σ = 1/ρ; current density J = I/A = σE
- Temperature: metals’ ρ rises with T (hot wires resist more)
Push twice the voltage through a wire and twice the current flows — for most materials, most of the time. This humble proportionality (Ohm’s law, 1827) plus one material number (resistivity) decides why copper wires carry power and rubber coatings save your life. Part 2 of the Current Electricity series.
- Ohm’s law: the proportion
- Resistance from geometry
- Resistivity: the material’s fingerprint
- Current density and microscopic Ohm
- Temperature effects
- Solved examples
- Common mistakes
- This physics in your daily life
- Practice set
- Recap
Ohm’s Law: The Proportion
| Letter | What it means (plain words) | Value / unit |
|---|---|---|
| V | potential difference across the conductor | volt |
| I | current through it | ampere |
| R | resistance — the V/I ratio | ohm (Ω) = V/A |
Resistance from Geometry
R = ρL/A: double the length, electrons face twice the obstacle course; double the area, twice the parallel lanes open. Geometry sets the form; the material fills in the number.
Resistivity: The Material’s Fingerprint
| Material | ρ (Ω·m) | Role |
|---|---|---|
| Silver | 1.6×10⁻⁸ | best metal (costly) |
| Copper | 1.7×10⁻⁸ | wiring standard |
| Aluminium | 2.8×10⁻⁸ | power lines (light) |
| Nichrome | ~10⁻⁶ | heaters (deliberately bad) |
| Rubber/glass | 10¹³+ | insulators |
Current Density and Microscopic Ohm
J = I/A (A/m²) and J = σE: the field drives the drift — Ohm’s law is Newton’s mechanics in disguise (field force → drift, collisions providing the friction that makes drift proportional, not accelerating).
Temperature Effects
In metals, hotter lattice = more collision obstacles → ρ rises roughly linearly. This is why bulb filaments read low resistance cold (inrush current surge) and 10× more at operating heat — and why semiconductor ρ FALLS with temperature (more carriers).
Solved Examples
I = V/R = 3 A.
✔
Answer: 3 A
L×2 and A×½ → R ×4: 4R.
Stretching is the exam’s favourite geometry trap — remember volume conservation.
✔
Answer: 4R
Along ℓ: R₁ = ρℓ/(wh). Along w: R₂ = ρw/(ℓh).
R₂/R₁ = w²/ℓ² — with ℓ = 2w, R₂ = R₁/4: direction matters in blocks.
✔
Answer: Quarter (for ℓ = 2w)
- Applying V = IR to non-ohmic devices. Diodes, transistors, electrolytes have no constant R — the ‘law’ is a material class, not a law of nature.
- Stretching without volume conservation. Stretched wire thins: L and A BOTH change — R goes as stretch².
- ρ vs R confusion. ρ belongs to the material; R depends on shape. Silver’s ρ is fixed whether it’s a wire or a block.
- Temperature amnesia in bulb problems. Cold filament ~1/10 of hot resistance: inrush current is ten-fold — a favourite exam and real-world fact.
This Physics in Your Daily Life
- Copper wiring everywhere — near-lowest ρ at human price: your home’s entire electrical network is a resistivity table decision.
- Overhead lines are aluminium — slightly worse ρ but a third the weight: engineering trades conductivity for sag (ρL/A in the sky).
- Nichrome toaster coils glow red — chosen for high resistivity: bad conductors make excellent heaters (Part 7’s topic).
- Bulbs flash bright then settle — the cold filament’s low R draws an inrush surge, then R climbs tenfold: the micro-second life of every incandescent switch-on.
- Thermistors in thermometers and battery packs — resistance reading temperature: ρ(T) turned into a sensor.
Electrons drifting through metal are like a person sprinting through a crowded fair: the field accelerates them, collisions with lattice atoms and defects brake them — the balance is a steady crawl (drift). Resistance IS the braking — the crowd’s difficulty rating of that particular corridor.
Copper vs nichrome: ρ differs ~60×. Same 1 m, 1 mm² wire: copper 0.017 Ω, nichrome ~1 Ω. Push 2 A: nichrome dumps 4 W of heat, copper 0.07 W: heaters are engineered bad conductors.
Draw the wire as a lane of toll booths (collision sites): more booths in series (longer L) → more total resistance; more parallel lanes (bigger A) → crowds split up. ρ is the booth density per lane-metre: the material’s crowd management style.
Practice set (answers hidden — try first)
(NEET-level) 9 V across 3 Ω: I =
(JEE Main-level) Wire stretched to 3× length (const. volume): R becomes
(NEET-level) Doubling both L and A:
(Concept) Ohm’s law is NOT obeyed by:
(JEE Main-level) ρ = 2×10⁻⁸, L = 100 m, A = 10⁻⁶ m²: R =
- V = IR for ohmic conductors
- R = ρL/A — geometry × material
- ρ: material fingerprint; σ = 1/ρ
- J = σE (microscopic Ohm)
- metals: ρ rises with T
- 🔁 Ohm’s law domain
- 🔁 R = ρL/A manipulations
- 🔁 resistivity table sense
- 🧠 Chant: ‘longer harder, fatter easier’.
- 🧠 Stretch rule: ‘stretch by n, R goes n²’.
- 🏠 Daily: aluminium lines trade ρ for weight.
- 🏠 Daily: bulb inrush = cold filament’s low R.
Quick revision
- Ohm’s law: V = IR for ohmic conductors at constant temperature — ratio V/I stays fixed
- Resistance R = ρL/A — longer wire, more resistance; fatter wire, less
- Resistivity ρ is the MATERIAL’s property: copper 1.7×10⁻⁸, rubber ~10¹³ Ω·m
- Conductivity σ = 1/ρ; current density J = I/A = σE
- Temperature: metals’ ρ rises with T (hot wires resist more)
- Ohm’s law: the proportion
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