Question

How long does it take electrons to get from

Answer 1

We need to find the time it takes an electron to move in the given circuit.

The time taken for electrons to reach the starting motor from the battery is 60.65 minutes.

I = Current = 134 A

$N_A$ = Avogadro's number = $6.022\times 10^{23}\ \text{mol}^{-1}$

A = Area = $38.9\ \text{mm}^2$

L = Length = 92.2 cm

$\rho$ = Density of copper = $8960\ \text{kg/m}^3$

M = Molar mass of copper = 63.5 g/mol

$n_v$ = Number of valence electrons of copper = 1

e = Charge of electron = $1.6\times 10^{-19}\ \text{C}$

Number of charge carriers per unit volume is given by

$n=\dfrac{\rho N_An_v}{M}\\\Rightarrow n=\dfrac{8960\times 6.022\times 10^{23}\times 1}{63.5\times 10^{-3}}\\\Rightarrow n=8.497\times 10^{28}\ \text{m}^{-3}$

Time taken is given by

$t=\dfrac{LAne}{I}\\\Rightarrow t=\dfrac{92.2\times 10^{-2}\times 38.9\times 10^{-6}\times 8.497\times 10^{28}\times 1.6\times 10^{-19}}{134}=3638.83\ \text{s}\\\Rightarrow t=\dfrac{3638.83}{60}=60.65\ \text{minutes}$

The time taken for electrons to reach the starting motor from the battery is 60.65 minutes.

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