How much current will flow through a 40.0 -$ { m }$ length of metal wire with a radius of $0.0 \mathrm {~mm}$ if it is connected to a power source supplying $16.0 \mathrm {~V} ?$ The resistivity of the metal is 1.68 × 10^-8 Ω ∙ m. A) 0 A B) 0 x 10⁸ A C) 0 nA

Question

Quizplus · Accepted Answer

To calculate the current that will flow through the wire, we need to use Ohm's law which states that current (I) is equal to voltage (V) divided by resistance (R), or I = V/R.

The resistance of a cylindrical wire is given by R = (ρL)/A, where ρ is the resistivity, L is the length of the wire, and A is the cross-sectional area of the wire.

The cross-sectional area of a wire is given by A = πr^2, where r is the radius of the wire.

Plugging in the given values, we get:

A = π(0.0000.1)^2 = 3.14 × 10^-8 m^2

R = (1.68 × 10^-8 Ω ∙ m)(40.0 m)/3.14 × 10^-8 m^2 = 2.15 Ω

Now, using Ohm's law, we get:

I = V/R = (16.0 V)/(2.15 Ω) = 7.44 A

However, the cross-sectional area of the wire is given as 0.0 mm, which is not possible. A wire cannot have zero radius or area.

Therefore, we can conclude that there is something wrong with the given information, and the correct answer is that no current will flow through the wire, which is choice (A).

How Much Current Will Flow Through a 40 m{ m }m

How Much Current Will Flow Through a 40 ${ m }$