Problem 74 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

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

Step 1: Write Down the Given Formula

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

Step 2: 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 \( \frac{1}{R_{1}} = \frac{1}{R} - \frac{1}{R_{2}} \).

Step 3: 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 \( \frac{1}{R_{1}} = \frac{R_{2} - R}{R*R_{2}} \).

Step 4: 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 \( R \).