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Hello students, we are given three resistances r1, r2 and r3.
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They are connected to a voltage of 5 volt.
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Now we need to find out in what manner the three resistances should be connected so as to maximize the power of the circuit.
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Now there are two ways to connect these three resistances.
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The first one is the parallel connection and second one is a series connection.
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However, there can be intermediate ways of combination of parallel and series circuits.
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However, it is out of the scope of this problem.
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Now, in a parallel connection, we see that the resistances are connected such that one end of all the resistances is connected to the same point and so are the other ends of the resistances.
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However, in a series connection, the resistances are connected end to end.
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The equivalent resistance in case of a parallel circuit is given by 1 upon r in parallel which is the equivalent resistance in a parallel connection equals to 1 upon r1 plus 1 upon r2 plus 1 upon r3.
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Let's say this is equation 1.
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Similarly, the resultant resistance in a series combination is given by rs equals.
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To r1 plus r2 plus r3.
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Let's say this is equation 2.
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Further from oms law we have v equals to i r.
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Let's say this is equation 3.
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Further, the power of the circuit is given as p equals to v into i.
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Let's say this is equation 4.
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Here, v is the voltage of the circuit, i is the current flowing in the circuit, p is the power and r is the resultant resistance of the circuit.
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Now we are given a few options out of which we have to select which one will maximize the power.
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The first option says that the resistances should be connected in parallel as a parallel combination maximization, maximizes the current which will maximize the power.
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Let's say if this is true.
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Now, the resultant resistance in a parallel circuit is always less than the individual resistances...