Problem 71 - College Algebra Essentials

Question

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$I R+I r=E \text { for } I$$

Step-by-Step Solution

Answer

The current \(I\) can be expressed as \(I = \frac{E}{R + r}\).

Step 1: Identify the variable to solve for

In the given equation \(I \cdot R + I \cdot r = E\), we need to solve for \(I\). This means we want to rewrite the equation in the form \(I = \frac{E}{R+r}\).

Step 2: Factor out the variable from the left side of the equation

First, factor out the common factor \(I\) on the left side of the equation, to get \(I \cdot (R + r) = E\).

Step 3: Divide by the remaining factor on the left side

Dividing both sides of the equation \(I \cdot (R + r) = E\) by \((R + r)\) to solve for \(I\), we get \(I = \frac{E}{R + r}\)