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 1.50V1.50\,\text{V}. Determine the ideal emf of the series-aiding string.

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Example 2: Effect of one reversed series cell

Six 1.50V1.50\,\text{V} cells are placed in one series string, but one cell is reversed. Determine the net emf.

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Example 3: Capacity and energy of cells in series

Four matched cells are each rated 3.60V3.60\,\text{V} and 2.50Ah2.50\,\text{Ah}. Determine the nominal voltage, capacity, and energy of a four-cell series string.

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Example 4: Capacity and energy of cells in parallel

Four matched cells are each rated 3.60V3.60\,\text{V} and 2.50Ah2.50\,\text{Ah}. Determine the nominal voltage, capacity, and energy when all four are connected in parallel.

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Example 5: Current from one real cell

A cell has emf E=1.50VE=1.50\,\text{V} and internal resistance r=0.50Ωr=0.50\,\Omega. It supplies an external load R=9.50ΩR=9.50\,\Omega. Determine current, terminal voltage, internal power loss, and load power.

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Example 6: Compare two real cells in series and parallel

Two identical cells each have E=1.50VE=1.50\,\text{V} and r=0.50Ωr=0.50\,\Omega. They supply a 10.0Ω10.0\,\Omega load. Determine the current for series and parallel arrangements.

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Example 7: Determine internal resistance from voltage sag

A cell has open-circuit voltage 1.55V1.55\,\text{V}. When it supplies 0.300A0.300\,\text{A}, its terminal voltage is 1.40V1.40\,\text{V}. Estimate its internal resistance.

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Example 8: Source efficiency under load

A cell with internal resistance 0.40Ω0.40\,\Omega supplies a 3.60Ω3.60\,\Omega load. Determine the source efficiency in the simple internal-resistance model.

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Example 9: C-rate and ideal runtime

A 4.00Ah4.00\,\text{Ah} cell supplies 2.00A2.00\,\text{A}. Determine the C-rate and the ideal capacity-based runtime.

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Example 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 3.70V3.70\,\text{V}, 2.00Ah2.00\,\text{Ah}, and has internal resistance 0.060Ω0.060\,\Omega. Determine nominal voltage, capacity, energy, and equivalent internal resistance.

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Example 11: Unequal cells connected in parallel

Two cells have open-circuit voltages 1.60V1.60\,\text{V} and 1.40V1.40\,\text{V}. Each has internal resistance 0.10Ω0.10\,\Omega. Estimate the initial circulating current if they are connected directly in parallel without an external load.

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Example 12: Compare measured and expected series voltage

Two cells measure 1.56V1.56\,\text{V} and 1.53V1.53\,\text{V} individually. Their measured series-aiding voltage is 3.06V3.06\,\text{V}. Determine the expected voltage and percentage difference.

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Problem-solving checks for cells and battery packs