Final answer:
To find the magnitude of the current when the drift velocity is 1.00 mm/s in a 14-gauge copper wire with a diameter of 1.628 mm, we can use the formula I = nqdAvd. By calculating the cross-sectional area of the wire and determining the number of free electrons per cubic meter, we can substitute these values into the formula to find the current. The correct option is A. 10.0 A.
Step-by-step explanation:
To find the magnitude of the current when the drift velocity is 1.00 mm/s in a 14-gauge copper wire with a diameter of 1.628 mm, we can use the formula:
I = nqdAvd
Where:
• I is the current
• n is the number of free electrons per cubic meter
• q is the charge of an electron (-1.60 x 10^-19 C)
• d is the diameter of the wire (1.628 mm)
• A is the cross-sectional area of the wire
• vd is the drift velocity
First, let's calculate the cross-sectional area of the wire:
A = πr2
Where r is half the diameter of the wire. In this case, r = 1.628 mm / 2 = 0.814 mm = 0.814 x 10^-3 m.
Substituting all the values into the formula, we get:
I = n(-1.60 x 10^-19 C)(π(0.814 x 10^-3 m)2)(1.00 x 10^-3 m/s)
Now we need to find the value of 'n'. The density of copper is 8.80 x 10^3 kg/m³ and the atomic mass of copper is 63.54 g/mol. Using Avogadro's number, 6.02 x 10^23 atoms/mol, we can determine 'n' as follows:
n = (8.80 x 10^3 kg/m³) / (63.54 g/mol) x (6.02 x 10^23 atoms/mol)
Plugging in the values, we can solve for 'n'.
After obtaining the value of 'n', we can substitute it back into the original formula to solve for 'I'. The correct option is A. 10.0 A.