A cylindrical wire of length L and radius r has a resistance R. The resistance of another wire of same material but having four times its length and half its radius will be:

Question

Question

This question was previously asked in

RRB ALP Electrician 22 Jan 2019 Official Paper (Shift 3)

Answer 1

Concept:

Resistance:

It is a measure of the opposition to current flow in an electrical circuit.
It is measured in ohms, symbolized by the Greek letter omega (Ω).
In the conducting wire, the resistance depends on the wire's length, cross-sectional area, and the material's resistivity.

Formula, Resistance, \(R=ρ \frac{L}{A}\), where ρ = resistivity of the material, A = cross-sectional area, L = length of the wire

Calculation:

Let's consider the length of the cylindrical wire is L and the radius of the wire is r.

The formula for the resistance of the conductor wire is given by,

\(R=ρ \frac{L}{A}=ρ \frac{L}{\pi r^2}\) . . . . . . . . . . . . . (1)

Now, the new length, L' = 4L

New radius, r' = r/2

So, \(R'=ρ \frac{(4L)}{\pi (r/2)^2}\)

\(R'=ρ \frac{4L}{\pi r^2/4}=16\rho \frac{L}{\pi r^2}\). . . . . . .(2)

From equations (1) and (2), we get

R' = 16R

Additional Information
Electrical Resistivity:

It is a fundamental property of a material that measures how strongly it resists electric current.
The SI unit of electrical resistivity is an ohm meter.