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Question

A 6Ω resistance wire is doubled on itself. Calculate the new resistance of the wire.


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Solution

Step 1: Given data and formula used

Given data:

  1. Resistance of the wire is R=6Ω

Consider the length of the wire be l and the area of the cross-section of the wire be A.

Formula:

The resistance of the wire is given by R=ρlA

Where ρ is the resistivity of the material of the wire.

When the wire is doubled on itself, the length of the wire becomes l/2 and the area of cross-section of the wire becomes 2A.

The new resistance of the wire becomes R'=ρl/22A

Step 2: Finding the formula of new resistance of the wire

Divide R' by R to calculate the new resistance of the wire.

R'R=ρl/22AρlAR'R=l4A×AlR'R=14R'=R4

Step 3: Calculating the new resistance of the wire

Substituting the value of resistance into the formula to calculate R'.

R'=6Ω4R'=1.5Ω

Thus, the new resistance of the wire is 1.5Ω.


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