Cells in Parallel and Unequal Sources
For n identical parallel cells, E_eq = E and r_eq = r/n. For unequal parallel cells, use Kirchhoff equations or conductance-weighted Thevenin equivalence with consistent polarity.
Why this shows up in the exam
Parallel battery banks · Unequal-emf source combinations · Series-versus-parallel current comparisons
Learn the idea
Parallel sources require branch-current equations; identical cells have unchanged emf and reduced internal resistance. Identical parallel cells share load current and behave like one emf with more conducting area internally. Unequal emfs can drive circulating current, so blindly averaging emfs is unsafe.
🧠 Memory hook: Identical parallel cells share current; unequal cells need equations.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- E_eq = E, r_eq = r/n — n identical cells in parallel
- E_th = (sum s_i E_i/r_i)/(sum 1/r_i) — open-circuit equivalent emf for unequal parallel branches
- r_th = 1/(sum 1/r_i) — equivalent internal resistance with ideal emfs suppressed
How to approach it
- 1Check whether cells are identical
- 2Mark polarity and branch currents
- 3Use KCL/KVL or Thevenin equivalence
Common slip-ups that cost marks
- •Adding parallel emfs
- •Averaging unequal emfs without resistance weights
- •Ignoring circulating current
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A cell of emf 6 V and internal resistance 1 ohm is connected to a 2 ohm resistor. Find the circuit current.
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