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Chapter 6

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.

Step-by-Step

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