Question

A 4 22 resistance wire is doubled on it. Calculate the new resistance of the wire.​

Answer 1

Correct Question :

A 4 ohm resistance wire is doubled on it. Calculate the new resistance of the wire.

AnswEr :

• The new resistance of the wire is 1 ohm.

Step-by-step explanation :

We're given with the resistance of the wire, that is, 4Ω . We're supposed to find the new resistance if the wire itself is doubled .

Now,

We know that if the wire is doubled then, the length of the wire will be halved and area would be doubled .

Before proceeding to the question, we need to know about the concept of Resistivity.

Resistivity of a wire is given by,

R = pL/A

Where,

• p is the resistivity of the material

• L is the length of the wire

• A is the area of cross-section of the wire

Let's assume R1 is the new resistance.

So,

➜ R1 = P(L/2) / 2A [As wire is doubled the length of the wire will be halved and area would be doubled ]

Taking the ratio of old and new resistance,

⇛ R1/R = [P × (L/2) / 2A] / [PL/A]

⇛ R1/R = 1/4

⇛ R1 = R/4

⇛ R1 = 4/4 [ As the value of R is 4Ω]

⇛ R1 = 1 Ω

Hence, the new resistance of the wire is 1 ohm .