Electrons Drifting in Copper

Q. A copper wire of cross-sectional area 1.0 × 10⁻⁷ m² carries a current of 1.5 A. Assume that each copper atom contributes roughly one conduction electron. The density of copper is 9.0 × 10³ kg/m³, and its atomic mass is 63.5 g/mol. What is the average drift speed of the conduction electrons, in mm/s? expects 1.1 mm/s

What the draft establishes

Fills in once a draft is checked.

The web of concepts

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The equations it used

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Check an answer

Q. A copper wire of cross-sectional area 1.0 × 10⁻⁷ m² $A = 1.0 \times 10^{−7}$ m² carries a current of 1.5 A $I = 1.5$ A. Assume that each copper atom contributes roughly one conduction electron. The density of copper is 9.0 × 10³ kg/m³ $ρ = 9.0 \times 10^{3}$ kg/m³, and its atomic mass is 63.5 g/mol $M = 63.5$ g/mol. What is the average drift speed of the conduction electrons, in mm/s?

The playground

Inputs

area

A

1e-07 m²

current

I

1.5 A

density

ρ

9000 kg/m³

molar mass

M

63.5 g/mol

Outputs

drift

v_{d}

The solution

Solved with DriftVelocity

Given

$A = 1.0 \times 10^{−7}$ m²
$I = 1.5$ A
$ρ = 9.0 \times 10^{3}$ kg/m³
$M = 63.5$ g/mol

Find $v_{d}$ .

Working

$M = 63.5$ g/mol $= 0.0635$ kg/mol
one free electron an atom(wire) $n = \frac{ρ \cdot N_{A}}{M}$
$n = \frac{9000 \cdot 6.02214076 \times 10^{23}}{0.0635}$
$n = 8.53531761 \times 10^{28}$ m⁻³
current from drift(wire) $I = n \cdot e \cdot A \cdot v_{d}$
$1.5 = 8.53531761 \times 10^{28} \cdot 1.60217663 \times 10^{−19} \cdot 1 \times 10^{−7} \cdot v_{d}$
$v_{d} = 1.097$ mm/s
$v_{d} = 0.00109688521$ m/s $= 1.09688521$ mm/s
$v_{d} \approx 1.1$ mm/sto 2 significant figures

Conclusion

Copper holds so many free electrons that a current of amperes needs them to drift only about a millimetre a second.

The Ruby

1require_relative "../physics"23question :electrons_drifting_in_copper do4  kind :numerical5  describes "A copper wire of cross-sectional area %{area} carries a current of %{current}. Assume that each copper " \6            "atom contributes roughly one conduction electron. The density of copper is %{density}, and its atomic " \7            "mass is %{molar_mass}. %{drift}, in mm/s?"8  given area: "1.0e-7 m2"9  given current: "1.5 A"10  given density: "9.0e3 kg/m3"11  given molar_mass: "63.5 g/mol"12  asks drift: "What is the average drift speed of the conduction electrons"13end

1require_relative "../questions/electrons_drifting_in_copper"2require_relative "../science/current_electricity/drift_velocity"34solve :electrons_drifting_in_copper, using: DriftVelocity do5  objects :wire67  take area: wire.cross_section8  take current: wire.current9  take density: wire.density10  take molar_mass: wire.molar_mass1112  drift = wire.drift_speed13  answer drift:, in: "mm/s", figures: 21415  conclusion "Copper holds so many free electrons that a current of amperes needs them to drift only about " \16             "a millimetre a second."17end

1require_relative "../solutions/electrons_drifting_in_copper"23play_with :electrons_drifting_in_copper do4  title "Electrons Drifting in Copper"5end

The laws

quantity	written	units	within	from
elementary charge	$e$	C	—	DriftVelocity
avogadro constant	$N_{A}$	mol⁻¹	—	DriftVelocity
current	$I$	A	—	DriftVelocity
cross section	$A$	m²	—	DriftVelocity
density	$ρ$	kg/m³	0 … ∞	DriftVelocity
molar mass	$M$	kg/mol	—	DriftVelocity
free electrons	$n$	m⁻³	—	DriftVelocity
drift speed	$v_{d}$	m/s	—	DriftVelocity
length of the conductor	$l$	m	—	DriftVelocity
drift time	$t$	s	—	DriftVelocity
free electrons of ground	$n_{g}$	m⁻³	—
density of ground	$ρ_{g}$	kg/m³	0 … ∞
molar mass of ground	$M_{g}$	kg/mol	—
free electrons of wire	$n$	m⁻³	—
density of wire	$ρ$	kg/m³	0 … ∞
molar mass of wire	$M$	kg/mol	—
current of ground	$I_{g}$	A	—
cross section of ground	$A_{g}$	m²	—
drift speed of ground	$v_{d,g}$	m/s	—
current of wire	$I$	A	—
cross section of wire	$A$	m²	—
drift speed of wire	$v_{d}$	m/s	—
length of the conductor of ground	$l_{g}$	m	—
drift time of ground	$t_{g}$	s	—
length of the conductor of wire	$l$	m	—
drift time of wire	$t$	s	—

n_{w} = \frac{ρ_{w} \cdot N_{A}}{M_{w}}

one free electron an atom

I_{w} = n_{w} \cdot e \cdot A_{w} \cdot v_{d,w}

current from drift

l_{w} = v_{d,w} \cdot t_{w}

drifting the length of the wire

n_{g} = \frac{ρ_{g} \cdot N_{A}}{M_{g}}

one free electron an atom(ground)

n = \frac{ρ \cdot N_{A}}{M}

one free electron an atom(wire)

I_{g} = n_{g} \cdot e \cdot A_{g} \cdot v_{d,g}

current from drift(ground)

I = n \cdot e \cdot A \cdot v_{d}

current from drift(wire)

l_{g} = v_{d,g} \cdot t_{g}

drifting the length of the wire(ground)

l = v_{d} \cdot t

drifting the length of the wire(wire)