Question

a 14-gauge copper wire has a diameter of 1.628 mm. what magnitude current flows when the drift velocity is 1.00 mm/s? (see example 20.3 (links to an external site.) for useful information.)

Answer 1

To calculate the magnitude of current flowing in a 14-gauge copper wire with a given drift velocity and diameter, use the formula I = nqAvd.

Step-by-step explanation:

The magnitude of current flowing in a 14-gauge copper wire with a diameter of 1.628 mm and a drift velocity of 1.00 mm/s can be calculated using the equation I = nqAvd. Given the diameter of the wire, we can calculate the area of cross-section using the formula A = π * (r^2), where r is the radius of the wire. The number of free electrons per unit volume, n, can be determined using the density of copper, Avogadro's number, and the atomic mass of copper. Finally, using the given drift velocity and the calculated values, we can find the magnitude of current flowing in the wire.

Answer 2

To find the magnitude of current flowing through a 14-gauge copper wire with a diameter of 1.628 mm when the drift velocity is 1.00 mm/s, we can use the formula I = nqAvd, where I is the current, n is the number of free electrons per cubic meter, q is the charge of an electron, A is the cross-sectional area of the wire, and vd is the drift velocity of the electrons.

Step-by-step explanation:

To find the magnitude of current flowing through a 14-gauge copper wire with a diameter of 1.628 mm when the drift velocity is 1.00 mm/s, we can use the formula I = nqAvd, where I is the current, n is the number of free electrons per cubic meter, q is the charge of an electron, A is the cross-sectional area of the wire, and vd is the drift velocity of the electrons.

First, let's calculate the cross-sectional area A. The formula for the area of a circle is A = πr^2, where r is the radius. Since the diameter of the wire is given, we can find the radius by dividing it by 2. With a diameter of 1.628 mm, the radius would be 0.814 mm or 0.000814 m.

Plugging the values into the equation, we get I = (n)(q)(πr^2)(vd). From Example 20.3, we know that the drift velocity of electrons in a 12-gauge wire carrying a 20.0-A current is 0.0033 m/s. We are asked to find the current for a 14-gauge wire, so we need to adjust the drift velocity accordingly. Assuming the drift velocity is inversely proportional to the wire diameter, we can calculate the adjusted drift velocity using the formula vd2 = (d1/d2)(vd1), where vd1 is the drift velocity of the 12-gauge wire, d1 is the diameter of the 12-gauge wire, d2 is the diameter of the 14-gauge wire, and vd2 is the adjusted drift velocity.

By substituting the values into the formula, we can find the adjusted drift velocity. Once we have the adjusted drift velocity, we can substitute the other known values into the equation to find the magnitude of the current flowing through the 14-gauge copper wire.