Question

If there are 10$^{18}$ electrons flowing across any cross section of a wire in 2 minutes what is the current in the wire?

Answer 1

Hint : Current(I) is defined as the rate of flow of charge $I = \dfrac{Q}{t}$ , where Q is the charge and t is time.
The charge on one electron is $1.6 \times {10^{ - 19}}C$ . Therefore the net charge in the wire due to the electrons can be calculated. The ratio of charge to time gives us the current in the wire.

Complete Step By Step Answer:
The number of electrons in any cross section of the wire is ${10^{18}}$ .
The time for which the current is to be measured is 2 minutes $= 2 \times 60\operatorname{s} = 120s$
We know that the charge on one electron is $1.6 \times {10^{ - 19}}C$ .
Therefore the total charge on electrons is ${10^{18}} \times 1.6 \times 1{0^{ - 19}}C = 1.6 \times {10^{ - 1}}C$ .
Current is defined as the rate of flow of charge through any cross section.
Therefore, it is the ratio of charge to time $I = \dfrac{Q}{t}$ .
Substituting the value of charge and time in the equation we get,
$I = \dfrac{{1.6 \times {{10}^{ - 1}}}}{{120}} = \dfrac{4}{3} \times {10^{ - 3}}A$
Therefore, the current in the wire is $1.33 \times {10^{ - 3}}A$ .

Note :
Current can be written as the ratio of charge to time. The charge on one electron should be remembered and is equal to $1.6 \times {10^{ - 19}}C$ . The electric current in a wire is a result of unidirectional motion of the electrically charged particles. When a potential difference is applied across the ends of the wire the free electrons align themselves to move in a particular direction thus causing current to be produced. Copper wire has the best electrical conductivity and allows almost all the electric current to flow through it without much resistance.