Chapter 4.1, Problem 71E

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Power The formula for the power output P of a battery is P = V I − R I 2 where V is the electromotive force in volts, R is the resistance in ohms, and Z 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. Assume that a 15-ampere fuse bounds the output in the interval 0 ≤ I ≤ 15 . Could the power output be increased by replacing the 15-ampere fuse with a20-ampere fuse? Explain.

To determine

To calculate: The current that corresponds to a maximum value of P and if the power output can be increased by a 20-ampere fuse.

Explanation

Given:

V=12Â volts,Â R=0.5Â ohm.

A 15-ampere fuse bounds the output in the interval 0â‰¤Iâ‰¤15.

Formula used:

The formula for power output,

P=VIâˆ’RI2

Calculation:

Consider the formula for power output,

P=VIâˆ’RI2

Substitute V=12Â volts,Â R=0.5Â ohm in above equation.

That is.,

P=12Iâˆ’0.5I2

Differentiate the function with respect to I

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started