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Chapter 0: Problem 37

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

Short Answer

Expert verified
The current, \(I\), is equal to the voltage, \(E\), divided by the total resistance, \((R + r)\), i.e., \(I = \frac{E}{(R + r)}\). This is a modification of Ohm's Law considering two resistances in series.

Step by step solution

01

Identify the equation and the unknown

The formula given is \(IR + Ir = E\), which is a variation of Ohm's Law where two resistances in series are considered, i.e., \(R + r = R'\) Where \(R'\) is the total resistance. Here, we have to solve it for \(I\).
02

Rearranging the equation

The goal is to isolate \(I\). Since \(I\) is a common factor in the left-hand side of the equation, we can factor it out: \(I(R + r) = E\).
03

Solving for \(I\)

To isolate \(I\), divide both sides of the equation by \((R + r)\): \(I = \frac{E}{(R + r)}\)

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