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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, a
Question
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.
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Physics
3 years
2021-08-22T13:26:36+00:00
2021-08-22T13:26:36+00:00 2 Answers
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Answers ( )
Answer:
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
Hope this Helps!!!
Explanation:
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