What is the smallest number of identical batteries with an emf of 1 V and an internal resistance of 1 Ohm that is necessary to use in order to achieve the maximum power at an external resistance of 18 Ohm? Maximum current should be 2 A. Comment: The batteries should be connected in n parallel groups with k batteries in series for each group.
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Answer:
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To find the smallest number of identical batteries needed to achieve maximum power at an external resistance of 18 Ohm, we need to use the formula for power in an electrical circuit, which is P = I² * R, where P is power, I is current, and R is resistance.
To achieve maximum power, we need to ensure that the internal resistance of the batteries matches the external resistance of 18 Ohm. This can be achieved by connecting the batteries in parallel groups with k batteries in series for each group.
Using Ohm's Law, we can calculate the current that each parallel group will provide. Since the maximum current is limited to 2 A, we need to divide this current by the number of parallel groups to ensure that each group is operating within the specified current limit.
Using these calculations, we can determine that we need at least 5 identical batteries with an emf of 1 V and an internal resistance of 1 Ohm to achieve maximum power at an external resistance of 18 Ohm, connected in 1 parallel group with 5 batteries in series.
Therefore, to achieve maximum power with an external resistance of 18 Ohm and a maximum current of 2 A, we need to connect 5 identical batteries in 1 parallel group with 5 batteries in series.
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