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 10⁶Ω are connected in parallel:

Let R be the equivalent resistance.

Therefore, equivalent resistance 1 Ω

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

Let R be the equivalent resistance.

Therefore, equivalent resistance = 0.999 Ω

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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.

(a) When 1 Ω and 106 Ω are connected in parallel: Let R be the equivalent resistance. Therefore, equivalent resistance 1 Ω (b) When 1 Ω, , and are connected in parallel: Let R be the equivalent resistance. Therefore, equivalent resistance = 0.999 Ω

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

(a) When 1 Ω and 10⁶Ω are connected in parallel:

Let R be the equivalent resistance.

Therefore, equivalent resistance 1 Ω

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

Let R be the equivalent resistance.

Therefore, equivalent resistance = 0.999 Ω