The formula for the power output P of a battery is P = VI – RI2, where V is the electromotive force in volts, R is the resistance in ohms, and I is the current in amperes. Find the current that corresponds to a maximum value of P in a battery for which V = 12 volts and R = 0.5 ohm.

The current that corresponds to a maximum value of P in a battery = 12 A.

That maximum power is 72 W.

Explanation:

The power output of a battery is given as

P = VI - RI²

V = 12 V

R = 0.5 ohm

P(I) = 12I - 0.5I²

The current that corresponds to a maximum value of P in the battery

P(I) = 12I - 0.5I²

For any function, at maximum point, the derivative of the dependent variable with respect to the independent variable is equal to 0.

At maximum power,

P'(I) = (dP/dI) = 0

P'(I) = (dP/dI) = 12 - I = 0

I = 12 A

That maximum power is

P(I=12) = 12(12) - 0.5(12²) = 144 - 72 = 72 W

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Explanation:

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