Question

Two of the three resistors in FIGURE EX28.22 are unknown but equal. The total resistance between points$aandb$is$75\Omega$is . What is the value of $R$?

Short answer

The value of $R$is $240\Omega$

Step-by-step solution

Given Information  

We have to find the value of$R$.

Simplify 

If two points and there are resistors connected at both ends of the points then it is called the resistors are connected in parallel. This is obvious when the resistors are aligned side by side. The potential difference across the resistors is the same in parallel connection. The equation shows the equivalent resistance for the parallel connection in the form

$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+....+\frac{1}{R_N}\left(1\right)$

We have three resistors in parallel where $R_1=200\Omega$and other two resistors are $R$and . We are given the equivalent circuit by $R_{eq}=75\Omega$. By equation $\left(1\right)$

$$\begin{gathered} \frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+....+\frac{1}{R_N} \\ \frac{1}{R}=\frac{1}{R_{eq}}\hspace{0.17em}-\frac{1}{R_1}\left(2\right) \\ R=1{\left(\frac{1}{R_{eq}}\hspace{0.17em}-\frac{1}{R_1}\right)}^{-1} \end{gathered}$$

Putting the value for $R_{eq}and{R}_1$into equationlocalid="1648916142131" $\left(2\right)$to get $R$by

$$\begin{gathered} R=2{\left(\frac{1}{R_{eq}}\hspace{0.17em}-\frac{1}{R_1}\right)}^{-1} \\ =2{\left(\frac{1}{75\Omega }\hspace{0.17em}-\frac{1}{2000\Omega }\right)}^{-1} \\ =240\Omega \end{gathered}$$