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Chapter 0: Problem 40

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 \( R_{1}=\frac{RR_{2}}{R_{2}-R} \). This formula can be used to find the individual resistance value in a parallel circuit given the total resistance and the known resistance of another resistor.

Step by step solution

01

Isolate \(R_{1}\) term

Start by isolating the \(R_{1}\)-related term to one side. This results in the equation \( \frac{1}{R_{1}}=\frac{1}{R} - \frac{1}{R_{2}} \)
02

Find common denominator

Next, find the common denominator for the right side of the equation. This will get \( \frac{1}{R_{1}}=\frac{R_{2}-R}{RR_{2}} \)
03

Take reciprocal

Finally, to solve for \(R_{1}\), take the reciprocal of both sides of the equation, which results in \( R_{1}=\frac{RR_{2}}{R_{2}-R} \).

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