Estimate the current density and drift velocity of conduction electrons in copper wire of cross section area…

Question

Estimate the current density and drift velocity of conduction electrons in copper wire of cross section area 0.0000002m carring current of 0.5A (assume that each copper atom contribute roughly one conduction electron,density of copper is 9000kg/m and it's atomic mass is 63.5g/mol

ScanSolve AI Tutor · Accepted Answer

Ili kukadiria msongamano wa mkondo na kasi ya mkengeuko ya elektroni za upitishaji katika waya wa shaba, tutatumia fomula zifuatazo:

Data Uliyopewa:

Mkondo (I) = $0.5 \text{ A}$
Eneo la msalaba (A) = $0.0000002 \text{ m}^2 = 2 \times 10^{-7} \text{ m}^2$
Msongamano wa shaba ( $\rho_{Cu}$ ) = $9000 \text{ kg/m}^3$
Masi ya atomiki ya shaba ( $M_{Cu}$ ) = $63.5 \text{ g/mol} = 0.0635 \text{ kg/mol}$
Kila atomu ya shaba huchangia elektroni moja ya upitishaji.
Chaji ya elektroni ( $e$ ) = $1.602 \times 10^{-19} \text{ C}$
Namba ya Avogadro ( $N_A$ ) = $6.022 \times 10^{23} \text{ mol}^{-1}$

Hesabu Msongamano wa Mkondo (Current Density, J).
Msongamano wa mkondo ni mkondo kwa kila eneo la msalaba.
$J = \frac{I}{A}$
Badilisha maadili:
$J = \frac{0.5 \text{ A}}{2 \times 10^{-7} \text{ m}^2}$ $J = 0.25 \times 10^7 \text{ A/m}^2$ $J = 2.5 \times 10^6 \text{ A/m}^2$
Hesabu Msongamano wa Namba ya Elektroni za Upitishaji (n).
Kwa kuwa kila atomu ya shaba huchangia elektroni moja ya upitishaji, msongamano wa namba ya elektroni ni sawa na msongamano wa namba ya atomu za shaba.
$n = \frac{\rho_{Cu}}{M_{Cu}} \times N_A$
Badilisha maadili:
$n = \frac{9000 \text{ kg/m}^3}{0.0635 \text{ kg/mol}} \times 6.022 \times 10^{23} \text{ mol}^{-1}$ $n = (141732.28 \text{ mol/m}^3) \times (6.022 \times 10^{23} \text{ mol}^{-1})$ $n \approx 8.53 \times 10^{28} \text{ m}^{-3}$
Hesabu Kasi ya Mkengeuko (Drift Velocity, $v_d$ ).
Uhusiano kati ya mkondo na kasi ya mkengeuko hutolewa na fomula:
$I = n A v_d e$
Panga upya fomula ili kupata $v_d$ :
$v_d = \frac{I}{n A e}$
Badilisha maadili:
$v_d = \frac{0.5 \text{ A}}{(8.53 \times 10^{28} \text{ m}^{-3}) \times (2 \times 10^{-7} \text{ m}^2) \times (1.602 \times 10^{-19} \text{ C})}$ $v_d = \frac{0.5}{(8.53 \times 2 \times 1.602) \times 10^{28 - 7 - 19}}$ $v_d = \frac{0.5}{27.32 \times 10^2}$ $v_d = \frac{0.5}{2732}$ $v_d \approx 0.000183 \text{ m/s}$ $v_d \approx 1.8 \times 10^{-4} \text{ m/s}$
Majibu:
- Msongamano wa mkondo ni $\boxed{2.5 \times 10^6 \text{ A/m}^2}$
- Kasi ya mkengeuko ni $\boxed{1.8 \times 10^{-4} \text{ m/s}}$

Estimate the current density and drift velocity of conduction electrons in copper wire of cross section area 0.0000002m carring current of 0.5A (assume that each copper atom contribute roughly one conduction electron,density of copper is 9000kg/m and it's atomic mass is 63.5g/mol

Answer

Step-by-step solution

Hesabu Msongamano wa Mkondo (Current Density, J).

Hesabu Msongamano wa Namba ya Elektroni za Upitishaji (n).

Hesabu Kasi ya Mkengeuko (Drift Velocity, $v_d$ ).

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More Physics Questions

Estimate the current density and drift velocity of conduction electrons in copper wire of cross section area 0.0000002m carring current of 0.5A (assume that each copper atom contribute roughly one conduction electron,density of copper is 9000kg/m and it's atomic mass is 63.5g/mol

Answer

Step-by-step solution

Hesabu Msongamano wa Mkondo (Current Density, J).

Hesabu Msongamano wa Namba ya Elektroni za Upitishaji (n).

Hesabu Kasi ya Mkengeuko (Drift Velocity, vdv_dvd​).

Try one yourself

Still stuck on this one?

More Physics Questions

Hesabu Kasi ya Mkengeuko (Drift Velocity, $v_d$ ).