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## Q. 6.11

Determine the values of $R_1, R_2, and R_3$ in Fig. 6.16 if $R_2 = 2R_1, R_3 = 2R_2$, and the total resistance is 16 kΩ.

## Verified Solution

Eq. (6.1) states

$\frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$

However, $R_2=2R_1\qquad and\qquad R_3=2R_2=2(2R_1)=4R_1$

so that   $\frac{1}{16k\Omega }=\frac{1}{R_1}+\frac{1}{2R_1}+\frac{1}{4R_1}$

and        $\frac{1}{16k\Omega }=\frac{1}{R_1}+\frac{1}{2}( \frac{1}{R_1})+\frac{1}{4}( \frac{1}{R_1})$

or          $\frac{1}{16k\Omega }=1.75\left(\frac{1}{R_1} \right)$

resulting in              $R_1=1.75(16k\Omega )=28k\Omega$

so that                      $R_2=2R_1=2(28k\Omega )=56k\Omega$

and                           $R_3=2R_2=2(56k\Omega )=112k\Omega$