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DC Sources
Construction and chemical action of primary and secondary cells; cells in series and parallel; internal resistance and its effect on terminal voltage.
DC sources — summary notes
FreeMain ideas
- Primary cells cannot be recharged; secondary cells can. Aircraft main batteries are secondary cells — lead-acid or nickel-cadmium.
- Every real source has internal resistance r. On load, terminal voltage is less than EMF because of the volt drop inside the cell: V = E − I·r.
- Cells in series add their voltages (capacity unchanged). Cells in parallel add their capacity in ampere-hours (voltage unchanged).
- Ni-Cd batteries are prone to thermal runaway — rising temperature lowers internal resistance, which raises charge current, which raises temperature further.
- ⚠ Exam trap: on load the terminal voltage is always less than the EMF; only on open circuit (I = 0) do they read the same.
Key formulas
- Terminal voltage
- V = E − I·r
- Cells in series
- E_total = n × E, r_total = n × r
- Cells in parallel
- E_total = E, capacity = n × Ah
Solved examples
A cell of EMF 12 V and internal resistance 0.5 Ω supplies 4 A. What is the terminal voltage?
V = E − I·r = 12 − (4 × 0.5) = 12 − 2 = 10 V.
Four 2 V cells of 30 Ah are connected in series. What are the resulting voltage and capacity?
Series adds voltage but not capacity: 8 V at 30 Ah.
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