Question

When the starter motor on a car is engaged, there is a 300 A cunent in the wires between the bauery and the motor. Suppose the wires are made of copper and have a total length of 1.0 m. What minimum diameter can the wires have if the voltage drop along the wires is to be less than 0.50 V? Problems

Answer 1

Answer:

diameter of transmission is 3.473 mm

Explanation:

given data

current = 300 A

total wire length = 1.0 m

voltage drop = 0.55 V

solution

as here Resistivity of copper is = 1.68 × $10^{-8}$ ohm- m

so we get here resistance of wire that is

resistance = $\frac{V}{I}$    ..............1

R = $\frac{0.55}{310}$  

R = 1.774 × $10^{-3}$  ohm

and now we get diameter of wire that is

R = $\frac{\rho l}{A}$    .............2

$\pi \frac{d^2}{4} = \frac{\rho l}{R}$    

d² = $\frac{4\rho l}{\pi R}$     ...............3

put here value

d² = $\frac{4\times 1.68\times 10^{-8} \times 1}{\pi \times 1.774\times 10^{-3}}$  

d = $\sqrt{12.064\times 10^{-6}}$

d = 3.473 × $10^{-3}$ m

d = 3.473 mm

so diameter of transmission is 3.473 mm