Understanding Electric Current and Electron Flow

This question asks us to determine the number of electrons that pass through a specific cross-section of a wire every second, given the current flowing through the wire and the charge carried by a single electron.

Electric current is essentially the flow of electric charge. When a current flows through a conductor like a wire, it's typically due to the movement of charge carriers. In most metals, these charge carriers are electrons.

Relating Current, Charge, and Number of Electrons

The definition of electric current (\(I\)) is the rate at which electric charge (\(Q\)) flows through a point or a cross-section per unit time (\(t\)). This can be written mathematically as:

\(I = \frac{Q}{t}\)

The total charge (\(Q\)) that flows through the wire is also related to the number of charge carriers (\(n\)) and the charge of each individual carrier (\(e\)). If \(n\) electrons pass through the section in time \(t\), the total charge \(Q\) is:

\(Q = n \times e\)

We can substitute this expression for \(Q\) into the formula for current:

\(I = \frac{n \times e}{t}\)

The question asks for the number of electrons passing per second. This means we need to find the value of \(\frac{n}{t}\) when \(t = 1\) second. From the rearranged formula, we get:

\(\frac{n}{t} = \frac{I}{e}\)

Applying Given Values to Calculate Electron Number

We are given the following information:

• Current (\(I\)) = 1 A (Ampere)
• Charge of one electron (\(e\)) = \(1.6 \times 10^{-19}\) C (Coulomb)
• Time (\(t\)) = 1 second (since we need electrons per second)

Now we can plug these values into the formula \(\frac{n}{t} = \frac{I}{e}\):

Number of electrons per second \(= \frac{1 \text{ A}}{1.6 \times 10^{-19} \text{ C}}\)

Let's perform the calculation:

\(\frac{n}{t} = \frac{1}{1.6 \times 10^{-19}}\)

\(\frac{n}{t} = \frac{1}{1.6} \times \frac{1}{10^{-19}}\)

Remember that \(\frac{1}{10^{-19}} = 10^{19}\). So,

\(\frac{n}{t} = \frac{1}{1.6} \times 10^{19}\)

To calculate \(\frac{1}{1.6}\), we can rewrite 1.6 as \(\frac{16}{10}\) or \(\frac{8}{5}\):

\(\frac{1}{1.6} = \frac{1}{\frac{16}{10}} = \frac{10}{16} = \frac{5}{8}\)

Now, convert \(\frac{5}{8}\) to a decimal:

\(\frac{5}{8} = 0.625\)

So, the number of electrons per second is:

\(\frac{n}{t} = 0.625 \times 10^{19}\)

This can also be written in standard scientific notation form by adjusting the decimal point. Move the decimal point one place to the right, which means we decrease the power of 10 by one:

\(0.625 \times 10^{19} = 6.25 \times 10^{18}\)

Therefore, \(6.25 \times 10^{18}\) electrons pass through the section of wire per second.

Summary of Calculation

Using the relationship \(I = n \times e / t\), and rearranging for \(n/t\), we get:

\(\frac{n}{t} = \frac{I}{e} = \frac{1 \text{ A}}{1.6 \times 10^{-19} \text{ C}}\)

Calculating the value:

\(\frac{n}{t} = \frac{1}{1.6} \times 10^{19} = 0.625 \times 10^{19} = 6.25 \times 10^{18}\)

Revision Table: Key Concepts in Electric Current

Additional Information on Charge Flow and Current

In conductors, current is typically the flow of negatively charged electrons. The conventional direction of current is defined as the direction positive charge would flow, which is opposite to the direction of electron flow.

• A current of 1 Ampere means that 1 Coulomb of charge passes through a point in the circuit every second.
• Since the charge of a single electron is very small (\(1.6 \times 10^{-19}\) C), a tremendous number of electrons must flow to constitute even a small current like 1 A.
• This calculation demonstrates the vast number of charge carriers involved in everyday electrical currents.

Understanding the relationship between macroscopic quantities like current and microscopic properties like the charge and number of electrons is fundamental in studying electricity.