Lesson 9 of 12 · 10 min
Cells in series and in parallel
NCERT § "Cells in Series and in Parallel"
The torch takes two cells. Put them in nose-to-tail and the bulb blazes; flip one round and it goes dark. Put them side by side and it barely changes.
The lesson in notes
In short
Two cells in series (positive of one to negative of the next) behave like one cell of emf ε_eq = ε₁ + ε₂ and internal resistance r_eq = r₁ + r₂.
If one cell in a series pair is reversed, its emf is subtracted: ε_eq = ε₁ − ε₂, while the internal resistances still add.
For n identical cells in series: emf nε and internal resistance nr.
Two cells in parallel (like terminals together) behave like one cell with ε_eq = (ε₁r₂ + ε₂r₁)/(r₁ + r₂) and r_eq = r₁r₂/(r₁ + r₂).
The parallel formula can be written 1/r_eq = 1/r₁ + 1/r₂ and ε_eq/r_eq = ε₁/r₁ + ε₂/r₂; if one cell is reversed, its ε changes sign.
For n identical cells in parallel: emf ε and internal resistance r/n.
When two cells of unequal emf are joined in parallel with no external load, a current circulates between them, driven through the lower-emf cell by the higher-emf one.