In Exercises 35–54, 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

Key Concepts

Reciprocal Relationships

In mathematics, a reciprocal relationship involves the inverse of a number or expression. For example, the reciprocal of a number 'x' is '1/x'. In the context of the given formula, the relationship between resistances in parallel circuits is expressed through reciprocals, indicating how the total resistance 'R' is affected by the individual resistances 'R1' and 'R2'.

Solving for a Variable

Solving for a variable means rearranging an equation to isolate the desired variable on one side. This process often involves using algebraic operations such as addition, subtraction, multiplication, and division. In the given formula, we need to manipulate the equation to express 'R1' in terms of 'R', 'R2', and their relationships, which is a fundamental skill in algebra.

Electrical Resistance in Parallel Circuits

The formula provided describes the total resistance in a parallel circuit, where multiple resistors are connected across the same voltage source. The total resistance 'R' is less than the smallest individual resistance, and the formula shows how the total resistance can be calculated using the individual resistances 'R1' and 'R2'. Understanding this concept is crucial for analyzing electrical circuits and their behavior.