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Solved Problem on Electric Current

A current of 2 A flows in a wire, knowing that the elementary charge is 1.6 × 10

Problema data

- electric current:
*i*= 2 A; - elementary charge:
*e*= 1.6 × 10^{−19}C; - time interval:
*t*= 1 s.

In figure 1 the electrons move from left to right across a cross-section, highlighted in gray, the

figure 1

Solution

The electric current is the rate at which charge flows through the cross-section

The electric current is the rate at which charge flows through the cross-section

\[ \bbox[#99CCFF,10px]
{i=\frac{\Delta q}{\Delta t}} \tag{I}
\]

The amount of charge that crosses a given cross-section, is the product of the number of charges, that crosses the
section, by the elementary charge
\[ \bbox[#99CCFF,10px]
{\Delta q=ne} \tag{II}
\]

substituting the expression (II) in (I), we have
\[
i=\frac{ne}{\Delta t}\\
n=\frac{i\;\Delta t}{e}
\]

substituting the data of the problem
\[
n=\frac{2 \times 1}{1.6 \times 10^{-19}}\\
n=\frac{2 \times 10^{19}}{1.6}
\]

\[ \bbox[#FFCCCC,10px]
{n=1.25 \times 10^{19}\;\rm{el{\acute e}trons}}
\]

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