Question

A wire of length 20 cm has a resistance of 20 Ω . If the wire is cut into 10 equal parts, then find the effective resistance when they are connected in parallel.​

Answer 1

Given : A wire of length 20 cm has a resistance of 20 Ω . Wire is cut into 10 equal parts,  

To find:  the effective resistance when they are connected in parallel.​

Solution:

A wire of length 20 cm has a resistance of 20 Ω

R ∝ Length

. Wire is cut into 10 equal parts,  

Hence Resistance of each part = 20/10  = 2 Ω

Now 10 resistance of 2  Ω are connected in parallel

Hence Effective resistance Reff

1/Reff = 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2

=> 1/Reff  = 10/2

=> 1/Reff = 5

=> Reff  = 1/5

=> Reff = 0.2 Ω

effective resistance when they are connected in parallel 0.2 Ω

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Answer 2

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➜A wire of length 20 cm has a resistance of 20 Ω

R ∝ Length

. Wire is cut into 10 equal parts,  

➜Hence Resistance of each part = 20/10  = 2 Ω

➜Now 10 resistance of 2  Ω are connected in parallel

Hence Effective resistance Reff

1/Reff = 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2

=> 1/Reff  = 10/2

=> 1/Reff = 5

=> Reff  = 1/5

=> Reff = 0.2 Ω

➜ effective resistance when they are connected in parallel 0.2 Ω

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