Question

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

Answer 1

Answer:

As 1 Ω and 1 to the power 6 Ω are connected parallel, the corresponding resistance R would be

I/R = 1/1+ 1/10 to the power 6. Therefore R = 1 Ω.

Again the corresponding resistance would be 1 Ω.  

For the second part 1 Ω, 10 Ω to the power 3 and 10 Ω to the power 6 are parallel.  Therefore  

I/R = 1/1 + 1/10 to the power 3 + 1/10 to the power 6.

Therefore R = 0.999 Ω

Answer 2

Answer:

A.) When 1Ω and $\bf{10}^{6}$ Ω are connected in parallel :

Let R be the equivalent resistance.

$\\ \therefore \sf \: \dfrac{1}{R} = \dfrac{1}{1} + \frac{1}{ {10}^{6} } \\ \\ \\ \implies \sf \: R = \frac{ {10}^{6} }{1 + {10}^{6} } \: \: \approx \: \: \frac{10 {}^{6} }{ {10}^{6} } \\ \\ \\ \implies \sf \blue{1 \: \Omega}$

Therefore, equivalent resistance ≈ 1Ω.

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B.) When 1Ω, 10³ Ω and $\bf{10}^{6}$ Ω are connected in parallel :

Let R be the equivalent resistance .

$\\ \sf \: \dfrac{1}{R} = \dfrac{1}{1} + \dfrac{1}{ {10}^{3} } +\dfrac{1}{ {10}^{6} } \\ \\ \\ \implies \sf \: \dfrac{ {10}^{6} + {10}^{3} + 1}{ {1}^{6} } \\ \\ \\ \implies \sf \: R = \dfrac{1000000}{1001001} \\ \\ \\ \implies \sf \green{0.999 \: \Omega}$

Therefore, equivalent resistance = 0.999 Ω.