/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 35 The power in an electrical syste... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Problem 35

The power in an electrical system varies jointly as the current and the square of the resistance. If the power is 100 watts when the current is 4 amps and the resistance is 5 ohms, what is the power when the current is 5 amps and the resistance is 6 ohms?

Short Answer

Expert verified
In the given electrical system, the power (P) varies jointly with the current (I) and the square of the resistance (R虏). Using the initial values of P=100 watts, I=4 amps, and R=5 ohms, we find the constant of variation (k) to be 1. With the new current of 5 amps and resistance of 6 ohms, the new power is \(P' = k \cdot I \cdot R^2 = 1 \cdot (5) \cdot (6^2) = 5 \cdot 36 = 180\) watts.

Step by step solution

01

Defining the Relationship

Given that the power (P) in an electrical system varies jointly as the current (I) and the square of the resistance (R虏), we can write the equation as: \[P = k \cdot I \cdot R^2\] where k is the constant of variation to be determined.
02

Determine the Constant of Variation k

We are given the initial power, current, and resistance values as P=100 watts, I=4 amps, and R=5 ohms. We can use these values to find the constant of variation (k) by plugging them into our equation: \[100 = k \cdot 4 \cdot (5^2)\]
03

Solve for k

Now we need to solve the equation for k: \[100 = k \cdot (4 \cdot 25)\] \[100 = k \cdot (100)\] \[k = \frac{100}{100}\] \[k = 1\]
04

Apply k to Find New Power

We are given the conditions for which we need to find the new power: I=5 amps, and R=6 ohms. Now we will use the value of k that we found in Step 3 to calculate the new power (P'): \[P' = 1 \cdot (5) \cdot (6^2)\]
05

Calculate P'

Solve for P' in the equation: \[P' = 1 \cdot (5) \cdot (36)\] \[P' = 5 \cdot 36\] \[P' = 180\]
06

Conclusion

When the current is 5 amps and the resistance is 6 ohms, the power in the electrical system is 180 watts.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use the transformation techniques to graph each of the following functions. $$h(x)=|x+1|-5$$

Determine the domain of each function. $$k(n)=\frac{8}{1-3 n}$$

Graph the following greatest integer functions. $$h(x)=[x-1]$$

Determine the domain of each function. $$r(t)=t^{3}-7 t^{2}+t+4$$

Graph the following piecewise functions. $$f(x)=\left\\{\begin{array}{cc}2 x-4, & x>1 \\\\-\frac{1}{3} x-\frac{5}{3}, & x \leq 1\end{array}\right.$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.