Question

a metal wire has a resistance of 60 ohm it is cut into 3 equal lengths find the equivalent resistance when two parts are connected in a parallel and third part is with series

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

Each resistance = 60/3 =20 ohm by using the formula of specific resistivity

now since first two are in parallel connection 1/R= 1/20 +1/20 =

R = 10 ohm

equivalent resistance = 10+20 ohm since the third connection is in series so the answer will be 30 ohm