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A battery of epsilon and internal resist...

A battery of `epsilon` and internal resistance `r` is used in a circuit with a variable external resistance `R`. Find the value of `R` for which the power consumed in `R` is maximum`.

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To find the value of the external resistance \( R \) for which the power consumed in \( R \) is maximum, we can follow these steps: ### Step 1: Write the expression for current \( I \) The current \( I \) flowing through the external resistance \( R \) can be expressed using Ohm's law. The total resistance in the circuit is the sum of the internal resistance \( r \) and the external resistance \( R \). Thus, the current \( I \) is given by: \[ I = \frac{\epsilon}{R + r} \] ...
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