Quick Recap — Circuits, Cells & Kirchhoff

  • Series: R=R1+R2+R = R_1 + R_2 + \ldots (same current). Parallel: 1R=1R1+1R2+\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \ldots (same voltage).
  • Cell: terminal voltage V=εIrV = \varepsilon - Ir; current I=εR+rI = \dfrac{\varepsilon}{R + r}.
  • Combinations of cells: nn in series give emf nεn\varepsilon; nn identical in parallel give emf ε\varepsilon and internal resistance r/nr/n.
  • Kirchhoff's laws: the junction rule (I=0\sum I = 0, charge conservation) and the loop rule (V=0\sum V = 0, energy conservation).
  • Wheatstone bridge is balanced when PQ=RS\dfrac{P}{Q} = \dfrac{R}{S}, so no current flows through the galvanometer.