Question

10 resistors 1 ohm each are joined in series and then in parallel. what will be the ratio of effective resistance of the first to that of the second?​

Answer 1

Answer:

100 : 1

Explanation:

When they are joined in series, the effective resistance is just their sum.

Eff. Resistance(R) = 1 + 1 + ... upto 10 terms

                       = 10

When they are joined in parallel, let the effective resistance be R, so:

1/R₁ = 1/1 + 1/1 + upto 10 terms

1/R₁ = 10         ⇒ R₁ = 1/10

Hence, ratio of eff. resistance of 1st to that of 2nd is:

⇒ R/R₁

⇒ (10)/(1/10)

⇒ 100 : 1

Answer 2

Answer:

When they are joined in series, the effective resistance is just their sum. Eff. Resistance(R) = 1 + 1 + upto 10 terms = 10

When they are joined in parallel, let the effective resistance be R, so: 1/R₁ = 10 ⇒ R₁ = 1/10

1/R₁ = 1/1 + 1/1 + upto 10 terms

Hence, ratio of eff. resistance of 1st to that

of 2nd is:

⇒ R/R₁

⇒ (10)/(1/10) ⇒ 100: 1

Explanation: