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Section 3.5

DC Sources

Construction and chemical action of primary and secondary cells; cells in series and parallel; internal resistance and its effect on terminal voltage.

Notes

DC sources, summary notes

Main 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

  1. 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.

  2. 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.

Mind map

DC sources concept map

DC Sources

Quiz

DC sources quiz

DC Sources, quiz

Ref 3.5Pass 75%

  1. 1. Three 1.5 V cells are connected as shown. The voltage across the two end terminals is:

    1.5 V1.5 V1.5 V
    4.5 V
    1.5 V
    0.5 V

  2. 2. Three 1.5 V cells are connected as shown. The voltage across the output terminals is:

    1.5 V1.5 V1.5 V
    1.5 V
    4.5 V
    0.5 V

  3. 3. A cell of EMF 12 V and internal resistance 0.5 Ω supplies 4 A. The terminal voltage is:

    10 V
    14 V
    12 V

  4. 4. A secondary cell is one that:

    Can be recharged
    Cannot be recharged
    Produces AC

  5. 5. Connecting cells in parallel increases the:

    Capacity in ampere-hours
    Terminal voltage
    Internal resistance

  6. 6. On load, the terminal voltage of a cell is:

    Less than its EMF
    Greater than its EMF
    Exactly equal to its EMF

  7. 7. Four 2 V cells connected in series give a total of:

    8 V
    2 V
    0.5 V

  8. 8. Thermal runaway is a particular hazard associated with:

    Nickel-cadmium batteries
    Primary dry cells
    Photocells

  9. 9. The terminal voltage of a cell equals its EMF only when:

    No current is being drawn
    The cell is fully discharged
    The cell is on maximum load

  10. 10. Two 6 V 20 Ah batteries connected in parallel give:

    6 V, 40 Ah
    12 V, 20 Ah
    12 V, 40 Ah

  11. 11. A cell of EMF 2 V and internal resistance 0.1 Ω is short-circuited. The current is:

    20 A
    2 A
    0.2 A

  12. 12. The capacity of a battery is measured in:

    Ampere-hours
    Volts
    Watts

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