Question

Find the length of the wire of diameter 2mm needed to prepare a coil of resistance 35ohm The specific resistance of material = 5.4 X10-5ohm m​

Answer 1

Answer:

Explanation:

Given R = 35 Ω, d= 2 mm , ρ = 5.4 x 10⁻⁵Ωm

Now Resistance R = ρ l /Α where l is length and A is area

Area of cross section = πr²

                                    =3.14 x 1 mm x 1 mm

                                    = 3.14 x 10⁻³ m x 10⁻³ m

                                    = 3.14 x 10⁻⁶ m

So l = R x A/ρ

       = 35 x 22 x 10⁻⁶ / 7 x 5.4 x 10 ⁻⁵

Cancelling out common factors we get,

l = 2.04 m

Answer 2

Given - Diameter of wire= 2 mm

Resistance = 35 ohm

Specific resistance = 5.4*10-⁵ ohm m

Find - Length of wire

Solution - The formula to be used in the calculation is Length = Resistance*Area/specific resistance

Converting diameter from millimetre to metre.

Diameter = 2 mm

Diameter = 2/1000

Diameter = 0.002 metre

Formula of area = πr²

Radius = Diameter/2

Radius = 0.002/2

Radius = 0.001 metre

Area = 3.14*10-⁶ metre²

Keeping the values in formula to calculate length of wire.

Length = 35*3.14*10-⁶/5.4*10-⁵

Length = 2.03 metres

Therefore, length of wire is 2.03 metres.