Question

Problems 79-84 list some formulas that occur in applications. Solve each formula for the indicated variable. $$ \text { Electricity } \frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}} \text { for } R $$

Short answer

R = \frac{R_1R_2}{R_1 + R_2}

Step-by-step solution

- Write Down the Given Formula

Start by writing down the given formula as it is: \[ \frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \]

- Find a Common Denominator

Combine the fractions on the right-hand side by finding a common denominator. In this case, the common denominator is \(R_1R_2\):\[ \frac{1}{R} = \frac{R_2 + R_1}{R_1R_2} \]

- Take the Reciprocal

To isolate \(R\) on one side, take the reciprocal of both sides of the equation:\[ R = \frac{R_1R_2}{R_1 + R_2} \]

Key concepts

Parallel Resistance Formula

The formula \(\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2}\) is used to find the equivalent resistance (\