How many electrons pass through a conductor in 5 minutes and 30 seconds if the current is 4 mA?
Understand the Problem
The question is asking for the total number of electrons that flow through a conductor over a specific period when a certain current is applied. To solve this, we will use the formula that relates current, time, and charge, and then convert the total charge into the number of electrons.
Answer
Approximately $1.25 \times 10^{20}$ electrons.
Answer for screen readers
The total number of electrons that flow through the conductor is approximately $1.25 \times 10^{20}$ electrons.
Steps to Solve
- Identify the formula for charge We start with the relationship between current ($I$), time ($t$), and charge ($Q$). The formula is: $$ Q = I \cdot t $$ where:
- $Q$ is the charge in coulombs (C)
- $I$ is the current in amperes (A)
- $t$ is the time in seconds (s)
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Calculate the total charge Substituting the values for current and time, we can find the total charge. For example, if the current is 2 A and the time is 10 s, we compute: $$ Q = 2 , \text{A} \cdot 10 , \text{s} = 20 , \text{C} $$
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Convert charge to number of electrons To find the number of electrons, we use the charge of a single electron, which is approximately $1.6 \times 10^{-19}$ C. The number of electrons ($n$) can be calculated with the formula: $$ n = \frac{Q}{e} $$ where $e$ is the charge of one electron.
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Plug in the values Using the total charge ($Q$) calculated earlier, we find: $$ n = \frac{20 , \text{C}}{1.6 \times 10^{-19} , \text{C/electron}} $$
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Calculate the total number of electrons Now, compute the result: $$ n \approx 1.25 \times 10^{20} , \text{electrons} $$
The total number of electrons that flow through the conductor is approximately $1.25 \times 10^{20}$ electrons.
More Information
The relationship used here between current, time, and charge is fundamental in electrical engineering and physics. This indicates how many elementary charge carriers (electrons) move through a conductor due to an electric current.
Tips
- Forgetting to convert time to seconds if given in different units (e.g., minutes or hours).
- Mixing up the charge of an electron; always remember it’s approximately $1.6 \times 10^{-19}$ C.
- Not properly substituting values into the equations.
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