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drek231 [11]
3 years ago
7

the electrical resistance of copper wire varies directly with its length and inversely with the square of the diameter of the wi

re. If a wire 30m long with a diameter of 3 mm has a resistance of 25 ohms, find the resistance of a wire 40m long with a diameter of 3.5 mm
Physics
1 answer:
leonid [27]3 years ago
8 0

Answer:24.47

Explanation:

Given

L_1=30 m

d_1=3 mm

R_1=25 \Omega

L_2=40 m

d_2=3.5 mm

we know Resistance R=\frac{\rho L}{A}

Where R=resistance

\rho =resistivity

L=Length

A=area of cross-section

A=\frac{\pi d^2}{4}

Thus R\propto \frac{L}{d^2}

therefore

R_1\propto \frac{L_1}{d_1^2}--------1

R_2\propto \frac{L_2}{d_2^2}--------2

divide 1 and 2 we get

\frac{R_1}{R_2}=\frac{L_1}{L_2}\times \frac{d_2^2}{d_1^2}

\frac{R_1}{R_2}=\frac{30}{40}\times \frac{3.5^2}{3^2}

R_2=25\times 0.734\times 1.33

R_2=24.47 \Omega

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