Question #255507

A 60 Ω resistor is made by winding platinum wire into a coil at 20°C. If the platinum has resistivity

r=10.4x10-8 Wm at 20°C and the platinum wire has a diameter of 0.10 mm, what length of wire is

needed?


1
Expert's answer
2021-10-25T17:52:09-0400

We use the formula

R=ρLAR=\frac{\rho*L}{A}

Where R= resistance in ohms

ρ\rho = resistivity in Wm

L = Length of wire

A = Cross sectional area

We have,

R=6Ω\Omega, ρ\rho =10.4 x 10-8Wm at 20°c

radius (r)= diameter2\frac{diameter}{2} = 0.10mm2\frac{0.10mm}{2} = 0.05mm

We convert to meters

0.05mm = 5 x 10-5m

Now, we find the Area

Area = π\pir2

Where π\pi = 227\frac{22}{7}, r = 5 x 10-5

Area = 227\frac{22}{7} * (5 x 10-5)2

= 227\frac{22}{7} * 2.5 x 10-9

= 7.86 x 10-9

Now, using the formula

R=ρLAR=\frac{\rho*L}{A}

Making L the subject of the formula

L=RAρL=\frac{R*A}{\rho}

= 607.8610910.4108\frac{60 *7.86*10^{-9}}{10.4 * 10^{-8}}

= 4.71610710.4108\frac{4.716*10^{-7}}{10.4*10^-{-8}}

= 1179260=4.53m(2d.p)\frac{1179}{260} = 4.53m (2 d.p)

Therefore, the length L= 4.53m



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