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The resistance, R (in ohms) of a wire varies directly with the length, L (in cm) of the wire, and inversely with the cross-sectional area, A (in cm^2). A 500 cm piece of wire with a radius of 0.2cm has a resistance of 0.025 ohm. Find an equation that relates these variables in the form of \(R = \frac {\square\cdot \pi\cdot L}{\square}\)

BillHicks1207  Apr 5, 2017
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The resistance, R (in ohms) of a wire varies directly with the length, L (in cm) of the wire, and inversely with the cross-sectional area, A (in cm^2). A 500 cm piece of wire with a radius of 0.2cm has a resistance of 0.025 ohm. Find an equation that relates these variables in the form of  \(R=\frac{\Box \cdot \pi \dot\ L}{\Box}\)

 

 

\(R=\rho\times \frac{L}{A}\)

 

\(R[\Omega]=\rho[\frac{\Omega \cdot mm^2}{m}]\times \frac{L[m]}{\pi\cdot r^2[mm^2]}\)

 

example

\(R=0,025\Omega\)

\(r=2 mm\)

\(L=0.5 m\)

 

\(\rho=\frac{A\cdot R}{L}=\frac{r^2\pi\cdot R}{L}=\frac{2^2mm^2\cdot \pi \cdot 0.025\Omega}{0.5m}\color{blue}=0.62832\frac{\Omega \cdot mm^2}{m}\)    [ stainless steel ]

 

laugh  !

asinus  Apr 5, 2017

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