Ch. 1 - Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problem 54

Chapter 2, Problem 54

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? 1/R = 1/R₁ + 1/R₂ for R₁

Verified step by step guidance

Start with the given formula:

\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}}

. The goal is to solve for

R_{1}

Subtract

\frac{1}{R_{2}}

from both sides of the equation to isolate the term involving

R_{1}

\frac{1}{R} - \frac{1}{R_{2}} = \frac{1}{R_{1}}

Simplify the left-hand side by finding a common denominator if necessary. This will combine the fractions into a single term:

\frac{expression}{denominator}

\frac{1}{R_{1}}

Take the reciprocal of both sides to solve for

R_{1}

. This step involves flipping the numerator and denominator on both sides of the equation.

Simplify the resulting expression to express

R_{1}

explicitly in terms of

R

and

R_{2}

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Algebraic Manipulation

Algebraic manipulation involves rearranging equations to isolate a specific variable. This process includes operations such as adding, subtracting, multiplying, or dividing both sides of the equation by the same value. In this case, solving for R1 requires moving terms around to express R1 in terms of R and R2.

Reciprocal Relationships

The formula 1/R = 1/R1 + 1/R2 describes the relationship between resistances in a parallel circuit, where the total resistance (R) is the reciprocal of the sum of the reciprocals of individual resistances (R1 and R2). Understanding reciprocals is crucial, as it helps in visualizing how combining resistances affects the overall circuit behavior.

Circuit Theory

Circuit theory is the study of how electrical components interact within a circuit. The formula provided is a fundamental concept in electrical engineering, specifically for parallel circuits, where the total resistance is less than the smallest individual resistance. Recognizing this formula helps in understanding how electrical systems function and how to calculate total resistance effectively.

Related Practice

Textbook Question

In Exercises 48–57, perform the indicated operations and write the result in standard form. 6/(5+i)

Textbook Question

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 3/(2x - 2) + 1/2 = 2/(x - 1)

Textbook Question

Solve each equation in Exercises 47–64 by completing the square. $x^{2} + 4 x + 1 = 0$

Textbook Question

Solve each equation in Exercises 47–64 by completing the square. $x^{2} - 5 x + 6 = 0$

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Textbook Question

Solve each equation in Exercises 41–60 by making an appropriate substitution. (x - 5)² - 4(x - 5) - 21 = 0

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Textbook Question

In Exercises 51–58, solve each compound inequality. - 11 < 2x - 1 ≤ - 5

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? 1/R = 1/R1 + 1/R2 for R1

Verified video answer for a similar problem:

Key Concepts

Algebraic Manipulation

Reciprocal Relationships

Circuit Theory

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? 1/R = 1/R₁ + 1/R₂ for R₁