Question

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Answer 1

Answer :-

(a) Equivalent resistance = 1 Ω

(b) Equivalent resistance = 0.999 Ω

Explanation :-

For number (a) :-

• 1st Resistance (R₁) = 1 Ω

• 2nd Resistance (R₂) = 10⁶ Ω

When two resistances are connceted in parallel, equivalent resistance is given by :-

R = R₁R₂/R₁ + R₂

⇒ R = (1 × 10⁶)/(1 + 10⁶)

⇒ R = 1000000/(1 + 1000000)

⇒ R = 1000000/1000001

⇒ R = 0.9999 Ω ≈ 1 Ω

For number (b) :-

• 1st resistance (R₁) = 1 Ω

• 2nd resistance (R₂) = 10³ Ω

• 3rd resistance (R₃) = 10⁶ Ω

For parallel connection of these three resistances, we get equivalent resistance as :-

1/R = 1/R₁ + 1/R₂ + 1/R₃

⇒ 1/R = 1/1 + 1/10³ + 1/10⁶

⇒ 1/R = (10⁶ + 10³ + 1)/10⁶

⇒ 1/R = 1001001/1000000

⇒ R = 1000000/1001001

⇒ R = 0.9990 Ω

Answer 2

Solution :-

We know that

R = R × R'/R + R'R

R = 1 × 10⁶/1 + 10⁶

• 10⁶  = 1000000

R = 1 + 1000000/1 + 1000000

R = 1000000/1000001

R = 0.99 Ω

Now

We know that

1/R = 1/R1 + 1/R2 + 1/R3

1/R = 1/1 + 1/10³ + 1/10⁶

1/R = 1/1 + 1/1000 + 1/10,00,000

1/R = 1000000 + 1000 + 1/1000000

1/R = 1001001/1000000

R × 1001001 = 1 × 1000000

1001001R = 1000000

R = 1000000/1001001

R = 0.9Ω

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