Question

Judge the equivalent resistance when the following are connected in parallel:
(a) 1$\Omega$ and ${10}^6\Omega$ (b) 1$\Omega$ and ${10}^3\Omega$, and ${10}^6\Omega$

Answer 1

a. $R_{eq}=1+\frac{1}{{10}^6}$

$=\frac{{10}^6+1}{{10}^6}$

$\approx \frac{{10}^6}{{10}^6}=1\Omega$

b. $\frac{1}{R_{eq}}=\frac{1}{1}+\frac{1}{1000}+\frac{1}{1000000}$

$=\frac{1000000+1000+1}{1000000}$

$R_{eq}=\frac{{10}^6}{1001001}$

$=0.9990\Omega =1\Omega$