Current Electricity — Ohm, Combinations & Power (Medium)

Quick Recap — Ohm's Law, Combinations & Power

• Ohm's law: $V=IR$; resistance $R=\rho\dfrac{L}{A}$ (so stretching a wire to $n$ times its length makes $R\to n^2R$). Drift velocity $v_d=\dfrac{I}{nAe}$.
• Combinations: series $R=R_1+R_2+\dots$ (same current); parallel $\dfrac{1}{R}=\sum\dfrac{1}{R_i}$ (same voltage).
• Power: $P=VI=I^2R=\dfrac{V^2}{R}$; energy in kWh $=$ (power in kW) $\times$ (hours). A bulb's resistance $=\dfrac{V_{rated}^2}{P_{rated}}$.
• Cells: terminal voltage $V=\varepsilon-Ir$ (discharging); $n$ cells in series give emf $n\varepsilon$; maximum power is delivered to a load when $R=r$.
• Rules: Kirchhoff's junction rule (charge conservation) and loop rule (energy conservation).

Worked mini-example. A 6 $\Omega$ and a 3 $\Omega$ resistor in parallel give $\dfrac{6\times3}{6+3}=2\ \Omega$; across 10 V they draw $I=\dfrac{10}{2}=5$ A.