What is the total power that serie and parallel array of batteries could provide?. Will it be the same for both arrays?

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What is the total power that serie and parallel array of batteries could provide?. Will it be the same for both arrays?

MIT 6.002 Circuits and Electronics, Spring 2007
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Yes. A single battery can only supply some maximum amount of current without overheating or sustaining a voltage drop due to internal resistance. Let's call that current I and the voltage the battery delivers V. So a single battery can deliver a power of P=VI Next consider n batteries in series. The voltage across these batteries is nV but still the maximum current is I since no individual battery can sustain a current higher than that so the maximum power delivered is P=nVI Now n batteries in parallel. The voltage across these batteries is V but each battery can deliver a current of I to the circuit. So the max power delivered is P=VnI Note that in a parallel combination, the batteries must be of the same chemical type otherwise the nominal voltage drops across each of them will be different and large currents could flow between them if they are connected in parallel.

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