Judge the equivalent resistance when the following are connected in parallel

Question: Judge the equivalent resistance when the following are connected in parallel −

(a) 1 Ω and 106Ω,

(b) 1 Ω and 103Ω and 106Ω.

Given that

(a) 1 Ω and 106Ω,

(b) 1 Ω and 103Ω and 106Ω

are connected in parallel.

Find out

Judge the equivalent resistance when the resistances  are connected in parallel

Solution

Let R be the equivalent resistance.

Given that 1 Ω and 106 Ω are connected in parallel then the equivalent resistance R will be

1/R = 1/1 + 1/ 106

= 106 + 1 / 106

= 1

R = 1 Ω
Equivalent resistance is 1 Ω
(b) 1 Ω and 103Ω and 106Ω are in parallel

1/R = 1/1 +  1/103 + 1/ 106

=106 + 1 + 10 3/ 106
R = 0.999 Ω
Therefore, equivalent resistance = 0.999 Ω

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