A steel wire of length LL and radius r1r1 has a resistance RR. A second steel wire has the same length but a radius r2r2 and a resistance of 2RR. Find the ratio r1/r2r1/r2. Express your answer to three significant figures.

r₁ / r₂ = 1.41

The resistance, R, of a wire is related to its resistivity, ρ, its crossectional area, A, and its length, L, as follows;

R = ρL/A         (i)

Where;

A = π x r²      [r = radius of the wire]

Therefore, equation (i) can be re-written as;

R =  ρL / (π x r²)         (ii)

(i) Now, For the first wire;

R = R

r = r₁

L = L

Substitute these values into equation (ii) as follows;

R =  ρL / (π x r₁²)

Make r₁ subject of the formula;

r₁² =  ρL / (π x R)

r₁ = √{ρL / (πR)]

(ii) Also, for the second wire;

R = 2R

r = r₂

L = L

Substitute these values into equation (ii) as follows;

2R =  ρL / (π x r₂²)

Make r₂ subject of the formula;

r₂² =  ρL / (π x 2R)

r₂ = √{ρL / (2πR)]

(iii) Now let's find the ratio of r₁ / r₂

r₁ = √{ρL / (πR)]

r₂ = √{ρL / (2πR)]

=> r₁ / r₂ = √ [  {ρL / (πR)]   / {ρL / (2πR)]   ]

=> r₁ / r₂ = √ [  {ρL / (πR)]   ÷  {ρL / (2πR)]   ]

=> r₁ / r₂ = √ [  {ρL / (πR)]   x  {2πR / (ρL)]   ]

=> r₁ / r₂ = √ [  {2πR / (πR)]  ]

=> r₁ / r₂ = √ [2]

=> r₁ / r₂ = √2

=> r₁ / r₂ = 1.41421

=> r₁ / r₂ = 1.41

Therefore, the ratio r₁ / r₂ = 1.41

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explanation:

wind is defined by the direction it blows from.   for example, a wind blowing from north to south is called a northerly wind.

electromagnetic shielding is the practice of reducing the electromagnetic field in a space by blocking the field with barriers made of conductive or magnetic materials. shielding is typically applied to enclosures to isolate electrical devices from their surroundings, and to cables to isolate wires from the environment through which the cable runs. electromagnetic shielding that blocks radio frequency electromagnetic radiation is also known as rf shielding.

the shielding can reduce the coupling of radio waves, electromagnetic fields and electrostatic fields. a conductive enclosure used to block electrostatic fields is also known as a faraday cage. the amount of reduction depends very much upon the material used, its thickness, the size of the shielded volume and the frequency of the fields of interest and the size, shape and orientation of apertures in a shield to an incident electromagnetic

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