Explanation Given : The power in the external resistor, P = E 2 R ( R + r ) 2 . Calculation: Consider the power in the external resistor, differentiate P with respect to R , d P d R = E 2 ( R + r ) 2 − E 2 R × 2 ( R + r ) ( R + r ) 4 = E 2 ( R + r ) − 2 E 2 R ( R + r ) 3 = E 2 R + E 2 r − 2 E 2 R ( R + r ) 3 = E 2 r − E 2 R ( R + r ) 3 For critical points, d P d R = 0 E 2 r − E 2 R ( R + r ) 3 = 0 E 2 r − E 2 R = 0 r − R = 0 r = R Differentiate d P d R with respect to R

Essential Calculus: Early Transcendentals

2nd Edition

ISBN: 9781133112280

Author: James Stewart

Publisher: Cengage Learning

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Chapter 4.5, Problem 33E

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To find: The maximum value of power where a resistor of R ohms is connected across a battery of E volts with internal resistance r ohms.

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Chapter 4.5, Problem 31E

Chapter 4.5, Problem 34E

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Essential Calculus: Early Transcendentals

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The maximum value of power where a resistor of R ohms is connected across a battery of E volts with internal resistance r ohms.

Solution Summary: The author calculates the maximum value of the power where a resistor of R ohms is connected across the battery of E volts with internal resistance.

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To find: The maximum value of power where a resistor of R ohms is connected across a battery of E volts with internal resistance r ohms.

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Chapter 4 Solutions