Physics, 03.03.2020 00:05 LillianMRucker

A coil is formed by winding 190 turns of insulated 16 gauge copper wire (diameter = 1.9 mm) in a single layer on a cylindrical form of radius 9.2 cm. What is the resistance of the coil? Neglect the thickness of the insulation. (Take the resistivity of copper to be 1.69 × 10-8 ohm-m.)

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Answer from: lovepink6524

Explanation:

The given data is as follows.

number of turns = n = 190 turns

radius = r = 9.2 cm = 0.092 m

diameter of copper wire = d = 1.9 mm

radius of copper wire = $r_{c}$ = $\frac{d}{2}$

= $\frac{1.9}{2}$

= $0.95 \times 10^{-3}$ m

where, A = cross sectional area of the wire

As, length of each turn of wire is 2pr where r is radius of the coil.

L = 190(2pr)

= $190 \times 6.28 \times 0.092 m$

= 109.77 m

The cross sectional area of the wire is as follows.

A = $\pi r^{2}_{c}$

= $3.14 (0.95 \times 10^{-3} m)^{2}$

= $2.83 \times 10^{-6} m^{2}$

It is given that resistivity of copper wire is $1.69 \times 10^{-8} \ohm$

R = $\rho \frac{L}{A}$

= $1.69 \times 10^{-8} \ohm \times \frac{109.77}{2.83 \times 10^{-6} m^{2}}$

= $65.53 \times 10^{-2} \ohm$

Thus, we can conclude that resistance of the coil is $65.53 \times 10^{-2} \ohm$ .

Answer from: iicekingmann

The resistance of the coil is 0.655 Ω

Explanation:

Given that,

Number of turns = 190 turns

Diameter of coil= 1.9 mm = 0.95 mm

Radius of single layer = 9.2 cm

Pressure = 16 gauge

We need to calculate the length of the wire

Using formula of length

$L=n2\pi r$

Where, n = number of turns

r = radius of cylinder

Put the value into the formula

$L=190\times2\pi\times9.2\times10^{-2}$

$L=109.8\ m$

We need to calculate the area of cross section

Using formula of area

$A=\pi\times r^2$

Put the value into the formula

$A=\pi\times(0.95\times10^{-3})^2$

$A=0.000002835\ m^2$

$A=2.83\times10^{-6}\ m^2$

We need to calculate the resistance of the coil

Using formula of resistivity

$R=\dfrac{\rho\times l}{A}$

Put the value into the formula

$R=\dfrac{1.69\times10^{-8}\times109.8}{2.83\times10^{-6}}$

$R=0.655\ \Omega$

Hence, The resistance of the coil is 0.655 Ω

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A coil is formed by winding 190 turns of insulated 16 gauge copper wire (diameter = 1.9 mm) in a sin...

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