Question

A piece of bare wire has a resistance of 1 ohms, if the wire is folded in half to make a new resistor which is half as long and has twice the across sectional area, what is the resistance of the new resistor?

Answer 1

The resistance of the nre resistor will be 1 Ω.

Given: A piece of bare wire has a resistance of 1 ohms, if the wire is folded in half to make a new resistor which is half as long and has twice the cross sectional area.

To find: The resistance of the nre resistor

Solution:

The electrical resistance of a circuit component or device is defined as the ratio of the voltage applied to the electric current which flows through it.

Resistance is measured in ohms.

Resistance can be calculated by the formula,

R = ρ L /A

where ρ is the resistivity which depends on the material. L is the length and A is the area.

Now as given in the question, Initial Resistance R₁ = 1 Ω

Let initial length is L₁ and initial area is A₁.

Then, R₁ = ρ L₁/A₁

Let final length is L₂ and final area is A₂. Now, final resistance R₂ will be,

R₂ = ρ L₂/A₂

Also, L₂ = 1/2 of L₁

and A₂ = 2A₁

R₂ = ρ x $\frac{L_{1} 2 }{2A_{1} }$

R₂ = ρ L₁/A₁

R₂ = R₁

Hence the resistance of new resistance will be 1 Ω.

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