Question

A 4 ohm resistance wire is doubled on it calculate the new resistance of the wire​

Answer 1

We consider wire is doubled on it means to fold the length of wire. It means its length will get half and area of cross section will get doubled.

∴ Let the resistance of the wire originally 'R' of length 'L' and area of cross-section 'A' with resistivity of material is 'p',

Then

R = p l/A = 4Ω

Now, for new arrangement,

p' = p

l' = l / 2

A' = 2A

Thus, 

R' = p' l'/A' = p (l /2) ÷ 2A = !/4 (p l / A) = 1/4R = 1/4 × 4 = 1Ω.

Answer 2

Given :-

• R = 4 ohms.

To be calculate :-

• New resistance of the wire.

Solution :-

We are given ,

R = 4 ohms .

When a wire is doubled on it , it's length would become half and area of cross would double . That is , a wire of length " l " and area of cross section A change to length l/2 and area of cross section 2A $.$

As you know ,

⇒ R = PL/A 

⇒ R' = P(L/2) / 2A

Where R' is the new resistance .

So,

R'/R = {P(L/2) / 2A} / {PL/A} 

After calculating , we get :-

 R' /R = ¼ 

⇒ R' = R/4

⇒ 4/4

⇒ 1 Ohm.

Hence , the required new resistance of the wire is 1 Ohm.

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