Current Electricity — Cells, Bridges & Networks (Medium)

Quick Recap — Cells, Bridges & Networks

• EMF & internal resistance: discharging $V=\varepsilon-Ir$; charging $V=\varepsilon+Ir$; short-circuit current $\dfrac{\varepsilon}{r}$.
• Wheatstone bridge (balanced): $\dfrac{P}{Q}=\dfrac{R}{S}$, and no current flows through the galvanometer. Metre bridge: unknown $X=R\dfrac{l}{100-l}$ (balance length $l$ cm).
• Potentiometer: compares emfs $\dfrac{\varepsilon_1}{\varepsilon_2}=\dfrac{l_1}{l_2}$; internal resistance $r=R\dfrac{l_1-l_2}{l_2}$. It draws no current at balance, so it reads true emf.
• Bulbs: in series the higher-resistance (lower-wattage) bulb glows brighter; in parallel the higher-wattage bulb is brighter.

Worked mini-example. A metre bridge balances at 40 cm with a known 4 $\Omega$ in the right gap: $X=R\dfrac{l}{100-l}=4\times\dfrac{40}{60}=2.67\ \Omega$.