Question

The electrical resistance of a​ wire, R, varies directly as its​ length, L, and inversely as its cross sectional​ area, A. If the resistance of a wire is 0.08 ohm when the length is 100 ft and its​ cross-sectional area is 0.05 in^2 ​, what is the resistance of a wire whose length is 4000 ft with a​ cross-sectional area of 0.02in^2 ​? ​a) Write the variation equation. (R=k(l/a) ​b) Determine the value of the quantity indicated. WILL MARK BRAINLIEST - 50PTS! NEED FAST - with work please so I understand how to do it, thank you:)

Answer 1

Step-by-step explanation:

(A)

Length of wire = 30.48 m

Area of cross section = 3.22 * 10 ^ -5 m^2

$R = k \frac{l}{a}$

$k = \frac{R \times a}{l} = \frac{0.08 \times 3.22 \times {10}^{ - 5} }{30.48} = 8.45 \times {10}^{ - 8} ohm \: m^{ - 1}$

(B) length of wire = 1219.2 m

Area of cross section = 1.29 * 10^-5 m^2

Resistance = 8.45 * 10^-8 * 1219.2 / 1.29 * 10^-5 = 7.98 Ohms