/*! 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 62 Solve each formula for the indic... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 62

Solve each formula for the indicated variable. $$U=\frac{1}{2} L I^{2}\( for \)L$ (physics)$$

Short Answer

Expert verified
We are given the formula \(U = \frac{1}{2} LI^2\), and we want to solve for \(L\). First, multiply both sides by \(2\) to eliminate the fraction, giving us \(2U = LI^2\). Next, divide both sides by \(I^2\) to isolate \(L\), resulting in \(L = \frac{2U}{I^2}\).

Step by step solution

01

Analyze the given formula

We are given the formula \(U = \frac{1}{2} LI^2\). Our goal is to isolate \(L\) on one side of the equation. We can see that the equation contains multiplication, so we will use division to isolate \(L\).
02

Multiply both sides by 2

To eliminate the fraction and make the manipulation easier, we can multiply both sides of the equation by \(2\): \[2U=2\left(\frac{1}{2}LI^2\right)\] This simplifies to: \[2U=LI^2\]
03

Divide both sides by \(I^2\)

Now, we need to eliminate the term \(I^2\) from the right side of the equation to isolate \(L\). We can do this by dividing both sides by \(I^2\): \[\frac{2U}{I^2}=\frac{LI^2}{I^2}\] This simplifies to: \[\frac{2U}{I^2}=L\]
04

Write the final result

We have now isolated \(L\) on one side of the equation, and the final result is: \[L=\frac{2U}{I^2}\] Now, we have successfully solved the equation for the variable \(L\).

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Physics Formulas
Physics formulas are like recipes in science. They tell us how different quantities relate to each other. One example is the formula for stored energy in an inductor, given by \( U = \frac{1}{2} L I^2 \). Here, \( U \) is the energy, \( L \) is the inductance, and \( I \) is the current. These formulas are vital because they help predict how systems behave in various conditions.
  • Understand Variables: Each symbol stands for a specific property, like energy or current.
  • Connections: The relationships in these formulas show how changing one quantity affects others.
Grasping these formulas requires a clear understanding of what each part signifies.
Variable Isolation
Isolating a variable means getting it by itself on one side of the equation. This is crucial in problem-solving since it lets us find the exact value of a variable. In our exercise, the task was to solve for \( L \), which involved a step-by-step approach. First, recognize which variable you need to isolate. In the formula \( U = \frac{1}{2} L I^2 \), this means focusing on \( L \).
Next, perform operations that gradually remove other terms or coefficients from that side of the equation. By doing this, you make the variable clear and easy to solve.
Multiplication and Division in Equations
Understanding how to manipulate equations with multiplication and division is key. In the exercise, we initially had \( U = \frac{1}{2} LI^2 \). To remove the fraction, multiply both sides by 2, transforming it to \( 2U = LI^2 \). This step simplifies the equation, allowing easier manipulation.
  • Multiply: Counteracts division or fractions. It can simplify complex terms.
  • Divide: Helps isolate variables by breaking down products, like dividing by \( I^2 \) to isolate \( L \).
Keeping track of these operations ensures an accurate solution by maintaining the equation's balance.

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

Solve. One-half cup of Ben and Jerry's Cherry Garcia Ice Cream has 260 calories. How many calories are in 3 cups of Cherry Garcia?

The area, \(A,\) of a triangle is \(A=\frac{1}{2} b h,\) where \(b=\) length of the base and \(h=\) height. The area, \(A,\) of a triangle is \(A=\frac{1}{2} b h,\) where \(b=\) length of the base and \(h=\) height. a) Solve \(A=\frac{1}{2} b h\) for \(h\) b) Find the height of the triangle that has an area of 30 in \(^{2}\) and a base of length 12 in.

Solve using the five "Steps for Solving Applied Problems." See Examples \(7-9\) Half of a number increased by ten is three. Find the number.

Solve using the five "Steps for Solving Applied Problems." See Examples \(7-9\) Three times a number is fifteen more than half the number. Find the number.

Write an equation and solve. Use the five "Steps for Solving Word Problems." In \(2002,\) Mia Hamm played in eight fewer U.S. National Team soccer matches than in \(2003 .\) During those 2 years she appeared in a total of 26 games. In how many games did she play in 2002 and in \(2003 ?\)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

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.