Question

What is the minimum resistance which can be made using five resistors each of 1/5 Ω? 

(a) 1/5 Ω 

(b) 1/25 Ω 

(c) 1/10 Ω 

(d) 25 Ω

Answer 1

The answer is (b) 1/25 Ω

Minimum resistance is obtained when resistors are connected parallel

1 /R = 5 + 5 + 5 +5 +5

= 25 Ω

R = 1/25

Answer 2

You know, equivalent resistance decreases when resistors are joined in parallel.
e.g., 1/Req = 1/R₁ + 1/R₂ + 1/R₃ + 1/R₄ + ....... + 1/Rn . While equivalent resistance increases when resistors are joined in series e.g., Req = R₁ + R₂ + R₃ + .... + Rn.
it Means, we can get minimum resistance when all the given resistors will join in parallel. And we can get maximum resistance when all the resistors will join in series .

∴ for finding minimum resistance , we have to join all resistors in parallel.
So , 1/Req = 1/(1/5) + 1/(1/5) + 1/(1/5) + 1/(1/5) + 1/(1/5)
1/Req = 5 + 5 + 5 + 5 + 5 = 25
Req = 1/25 Ω

Hence , minimum resistance = 1/25 Ω