Experiment 12: Cells in Series and Parallel — Worked Examples
These examples begin with ideal cell arrangements and progress to real-source behavior, capacity, energy, discharge rate, efficiency, mismatch, and series-parallel pack design.
Example 1: Series-aiding voltage
Six identical cells each have emf . Determine the ideal emf of the series-aiding string.
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0 of 3 Steps CompletedExample 2: Effect of one reversed series cell
Six cells are placed in one series string, but one cell is reversed. Determine the net emf.
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0 of 3 Steps CompletedExample 3: Capacity and energy of cells in series
Four matched cells are each rated and . Determine the nominal voltage, capacity, and energy of a four-cell series string.
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Four matched cells are each rated and . Determine the nominal voltage, capacity, and energy when all four are connected in parallel.
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0 of 4 Steps CompletedExample 5: Current from one real cell
A cell has emf and internal resistance . It supplies an external load . Determine current, terminal voltage, internal power loss, and load power.
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Two identical cells each have and . They supply a load. Determine the current for series and parallel arrangements.
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A cell has open-circuit voltage . When it supplies , its terminal voltage is . Estimate its internal resistance.
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A cell with internal resistance supplies a load. Determine the source efficiency in the simple internal-resistance model.
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A cell supplies . Determine the C-rate and the ideal capacity-based runtime.
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0 of 3 Steps CompletedExample 10: Analyze a 3S2P battery pack
Six matched cells are arranged as three cells in series per string and two equal strings in parallel. Each cell is rated , , and has internal resistance . Determine nominal voltage, capacity, energy, and equivalent internal resistance.
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Two cells have open-circuit voltages and . Each has internal resistance . Estimate the initial circulating current if they are connected directly in parallel without an external load.
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Two cells measure and individually. Their measured series-aiding voltage is . Determine the expected voltage and percentage difference.
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- Draw cell polarity before adding or subtracting emfs.
- Separate voltage, ampere-hour capacity, watt-hour energy, and current capability; they are not interchangeable.
- Add internal resistances in series and combine them in parallel.
- Include internal resistance when terminal voltage or voltage sag matters.
- Use matched cells when applying ideal parallel formulas.
- Check that only equal-voltage series strings are placed in parallel.
- Distinguish ideal runtime estimates from actual chemistry-dependent performance.
- Never use a short-circuit test to determine maximum current.