Solved Problem on Electric Current
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A current of 2 A flows in a wire, knowing that the elementary charge is 1.6 × 10−19. How many electrons passing through a cross-section of the wire during a time interval of 1 s?

Problema data
  • electric current:    i = 2 A;
  • elementary charge:    e = 1.6 × 10−19 C;
  • time interval:    t = 1 s.
Problem diagram

In figure 1 the electrons move from left to right across a cross-section, highlighted in gray, the conventional current ( i ) is indicated in the direction opposite to the movement of the electrons.

Electrons are flowing in a segment of a wire passing through the cross-section.
figure 1


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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