Judge the equivalent resistance when the following are connected in parallel − (a) 1 Ω and 10^{6}Ω, (b) 1 Ω and 10^{3}Ω and 10^{6}Ω.

^{6}Ω, (b) 1 Ω and 10^{3}Ω and 10^{6}Ω.

(a) When 1 Ω and 10^{6} Ω are connected in parallel:

Let *R* be the equivalent resistance.

\(\therefore \frac{1}{R} = \frac{1}{1}+\frac{1}{10^6} \\ \)

\(R=\frac{10^6}{1+10^6} \simeq \frac{10^6}{10^6}=1 \Omega\)

Therefore, equivalent resistance ≈ 1 Ω

(b) When 1Ω, 103 Ω and 106 Ω are connected in parallel:

Let *R* be the equivalent resistance.

\(\frac{1}{R}=\frac{1}{1}+\frac{1}{10^3}+\frac{1}{10^6}\frac{10^6 +10^3+1}{10^6} \\ \)

\(R=\frac{1000000}{1001001}= 0.999\Omega\)

Therefore, equivalent resistance = 0.999 Ω