Question

How much current will be flowing through a 40.0 m length of cylindrical metal wire with radius 4.0 mm if it is connected to a source supplying 16.0 V? The resistivity of this metal is 1.68 × 10-8 Ω · m.
of this metal is 1.68 × 10-8 Ω · m.
a. 68 nA.
b. 9.5 × 108 A.
c. 1200 A.
d. 710 A.

Answer 1

Answer:

Current, I = 1200 A                                    

Explanation:

It is given that,

Length of the cylinder, l = 40 m

Radius of the metal wire, r = 4 mm = 0.004 m

Voltage source, V = 16 V

Resistivity of metal, $\rho=1.68\times 10^{-8}\ \Omega-m$    

We know that the resistivity of any metal is given by the formula as :

$R=\rho \dfrac{l}{A}$

$R=1.68\times 10^{-8}\times \dfrac{40}{\pi (0.004)^2}$

R = 0.01336 ohms

Using ohm's law :

$R=\dfrac{V}{I}$

$I=\dfrac{V}{R}$

$I=\dfrac{16}{0.01336}$

I = 1197.60 A

or

I = 1200 A

So, the current flowing in the cylindrical wire is 1200 A. Hence, this is the required solution.