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Question
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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Solution
(a) When 1 Ω and 106 Ω are connected in parallel:
Let R be the equivalent resistance.
R2 = 106 Ω .....[given]
`1/"R" = 1/1 + 1/10^6`
`1/"R" = (10^6 + 1)/10^6`
R = `10^6/(1 + 10^6)` ≈ 1 Ω
R ≈ 1 Ω
Therefore, equivalent resistance ≈ 1 Ω
(b) When 1Ω, 103 Ω and 106 Ω are connected in parallel:
Let R be the equivalent resistance.
`1/"R" = 1/"R"_1 + 1/"R"_2 + 1/"R"_3`
R1 = 1 Ω .....[given]
R2 = 103 Ω
R3 = 106 Ω
`1/"R" = 1/1 + 1/10^3 + 1/10^6`
`1/"R" = (10^6 + 10^3 + 1)/10^6`
`1/"R" = 1001001/1000000`
R = `1000000/1001001` ≈ 0.999 Ω ≈ 1 Ω
R ≈ 1 Ω
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