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.
Chapter 6
Q. 6.11
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