Question

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

Answer 1

Given:

The length of the wire initially = 20 cm

Tge resistance of the wire initially = 20 ohms

Number of parts in which the wire is cut= 10

To find:

Effective resistance when the wires are connected in parallel.

Solution:

If the wire ia cut into 10 parts then the resistance of each part will be 1/10th of the wire. Therefore resistance will be:

R = 20/10 = 2

If the wires are connected in parallel then effective resistance is:

1/R' = 1/R + 1/R. . . . . .10 times

= 10/R

= 10/2

= 5

R' = 1/5 ohms

Therefore the effective resistance us 1/5 ohms.

Answer 2

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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