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Chapter 1: Problem 74

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}} \text { for } R_{1}$$

Short Answer

Expert verified
The formula for \( R_{1} \) is \( R_{1} = \frac{R*R_{2}}{R_{2} - R} \), provided \( R_{2} \) is not equal to \( R \).

Step by step solution

01

Write Down the Given Formula

Start with the given formula, which is: \( \frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} \).
02

Isolate the Term with \( R_{1} \)

To make \( R_{1} \) the subject of the formula, first isolate \( \frac{1}{R_{1}} \) by subtracting \( \frac{1}{R_{2}} \) from both sides. This gives \( \frac{1}{R_{1}} = \frac{1}{R} - \frac{1}{R_{2}} \).
03

Find a Common Denominator

Combine the two fractions on the right hand side by finding a common denominator, which is \( R*R_{2} \). \This gives us \( \frac{1}{R_{1}} = \frac{R_{2} - R}{R*R_{2}} \).
04

Take the Reciprocal

To get \( R_{1} \), take the reciprocal of both sides. This gives \( R_{1} = \frac{R*R_{2}}{R_{2} - R} \). Be careful as division by zero is undefined. Therefore, in physical applications, a check must be made that \( R_{2} \) is not equal to \( R \).

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