Question

A metal wire has a resistance of 60 Ω. It is cut into three equal lengths. Find the equivalent resistance

Answer 1

We know, resistance of a wire is directly proportional to its length .

e.g., R\propto∝ L [∵R = ρL/A, here R is resistance , L is the length of wire , A is base area of wire and ρ is resistivity of material of wire ]

So, if we divide wire of resistance 60Ω into 3 parts then, resistance of each part will be 60/3Ω = 20Ω

Now, A/C to question,

All the three resistors , 20Ω are joined in parallel combination.

So, Equivalent resistance ,Req :

1/Req = 1/R₁ + 1/R₂ + 1/R₃

⇒ 1/Req = 1/20Ω + 1/20Ω + 1/20Ω

Req = 20/3Ω = 6.67Ω

Answer 2

Resistance will be 20Ω