Example from Physics, 19.2 Series Circuits

Determine the Unknown Resistance

The circuit shown in figure below contains three resistors of known value and a third element whose resistance $R_{3}$ is unknown. Given that the equivalent resistance for the entire circuit is 150 $Ω$ , what is the resistance $R_{3}$ ?

A circuit diagram shows a battery and four resistors; only the resistances of three of the resistors are given.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
The four resistances in this circuit are connected in series, so we know that they must add up to give the equivalent resistance. We can use this to find the unknown resistance $R_{3}$ .
Solution
For four resistances in series, the equation for the equivalent resistance of resistors in series takes the form

$R_{equiv} = R_{1} + R_{2} + R_{3} + R_{4} .$
19.19

Solving for R3 and inserting the known values gives

$\begin{matrix} R_{3} & = & R_{equiv} - R_{1} - R_{2} - R_{4} \\ = & 150 Ω - 10 Ω - 25 Ω - 15 Ω \\ = & 100 Ω. \end{matrix}$
19.20

0 of 2 steps open

How did it go?

Strategy

Solution