## An 18-gauge copper wire (diameter 1.02 mm) carries a current with a current density of 1.40×106 A/m2 . Copper has 8.5×1028 free electrons pe

Question

An 18-gauge copper wire (diameter 1.02 mm) carries a current with a current density of 1.40×106 A/m2 . Copper has 8.5×1028 free electrons per cubic meter

Calculate the current in the wire

Calculate the drift velocity of electrons in the wire.

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1 year 2021-09-03T16:13:52+00:00 1 Answers 860 views 0

Part (a) current in the wire is 1.144 A

Part (b) the drift velocity of electrons in the wire is 1.028 x 10⁻⁴ m/s

Explanation:

Given;

diameter d  = 1.02 mm

current density J = 1.40×10⁶ A/m²

number of electron = 8.5×10²⁸ electrons

Part (a) Current in the wire

I = J×A

Where A is area of the wire;

$$A = \frac{\pi d^2}{4} \\\\A = \frac{\pi (1.02X10^{-3})^2}{4} = 8.1723 X10^{-7} m^2$$

I = 1.40 x 10⁶ x 8.1723 x 10⁻⁷

I = 1.144 A

Part (b) the drift velocity of electrons in the wire

$$V = \frac{J}{nq} = \frac{1.4X10^6}{8.5X10^{28} X 1.602X10^{-19}} = 1.028 X10^{-4} m/s$$