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Judge the equivalent resistance when the following are connected in parallel − (a) 1 Ω and 106Ω, (b) 1 Ω and 103Ω and 106Ω.

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(a) When 1 Ω and 106 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

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