Ohm’s Law 🚀

Georg Simon Ohm found in 1828 that the potential difference V across a conductor is directly proportional to the current I flowing through it: \(V \propto I \Rightarrow V = R\,I\) — where R is the resistance measured in ohms (Ω). :contentReference[oaicite:0]{index=0}

What resistance really means 😎

  • Resistance depends on size: doubling a conductor’s length doubles its resistance ⇒ \(R \propto \ell\). :contentReference[oaicite:1]{index=1}
  • Resistance depends on thickness: halving the cross-sectional area doubles the resistance ⇒ \(R \propto \frac{1}{A}\). :contentReference[oaicite:2]{index=2}
  • Putting both ideas together gives the super-useful formula \(R = \rho\,\dfrac{\ell}{A}\) where ρ (rho) is the resistivity — a material property, not a size property. :contentReference[oaicite:3]{index=3}

Linking volts, amps, and material 🌐

Insert \(R = \rho\frac{\ell}{A}\) into \(V = R\,I\) and you get a handy working form: \(V = I\,\rho\,\dfrac{\ell}{A}\). :contentReference[oaicite:4]{index=4} So, for a given material (fixed ρ), long or thin wires need a bigger push (voltage) to drive the same current.

Current density & electric field ⚡

  • Current density: \(j = \dfrac{I}{A}\) (amps per square metre). :contentReference[oaicite:5]{index=5}
  • For a uniform field, the potential drop is \(V = E\,\ell\). Combining with Ohm’s law gives \(E = \rho\,j\) or \(j = \sigma\,E\) where \(\sigma = \dfrac{1}{\rho}\) is the conductivity. :contentReference[oaicite:6]{index=6}

Why electrons drift (quick peek) 👀

Electrons bounce around randomly, but an applied electric field nudges them so their average motion (called drift) is opposite the field direction. This steady drift is what the equations above describe. :contentReference[oaicite:7]{index=7}

High-yield ideas for NEET 🎯

  1. Core statement: \(V = R\,I\) and the definition of resistance (Ω).
  2. Dimension rule: \(R = \rho\,\dfrac{\ell}{A}\) — how length and area change resistance.
  3. Material identity: Resistivity ρ vs. Conductivity σ (\(\sigma = 1/\rho\)).
  4. Field relation: \(E = \rho\,j\) or \(j = \sigma\,E\) linking microscopic field to macroscopic current.
  5. Current density trick: \(j = \dfrac{I}{A}\) — converts big-picture current into a local quantity.

Keep these nuggets 🔑 in mind, practice some quick calculations, and you’ll breeze through related NEET problems! 🌟