A conductor carries current of 0.2A. Find the amount of charge that will pass to the cross section of the conductor in 30 seconds. How many electrons will flow if the charge of electrons is [tex]$1.6 \times 10^{-19} C$[/tex]?
Answer (1)
Calculate the total charge using the formula Q = I × t , where I = 0.2 A and t = 30 s , resulting in Q = 6 C .
Calculate the number of electrons using the formula n = e Q , where Q = 6 C and e = 1.6 × 1 0 − 19 C .
Substitute the values to find n = 1.6 × 1 0 − 19 6 = 3.75 × 1 0 19 .
The amount of charge is 6 Coulombs and the number of electrons is 3.75 × 1 0 19 , so the final answer is 3.75 × 1 0 19 .
Explanation
Understanding the Problem We are given a conductor carrying a current of 0.2A. We need to find the amount of charge that passes through the cross-section of the conductor in 30 seconds and the number of electrons that flow if the charge of each electron is 1.6 × 1 0 − 19 C.
Calculating the Total Charge First, we need to calculate the total charge (Q) that passes through the conductor. We can use the formula:
Q = I × t
where:
Q is the total charge in Coulombs (C)
I is the current in Amperes (A)
t is the time in seconds (s)
Substituting the Values Now, we substitute the given values into the formula:
Q = 0.2 A × 30 s = 6 C
So, the total charge that passes through the conductor is 6 Coulombs.
Calculating the Number of Electrons Next, we need to find the number of electrons (n) that make up this charge. We can use the formula:
n = e Q
where:
n is the number of electrons
Q is the total charge in Coulombs (C)
e is the charge of a single electron, which is 1.6 × 1 0 − 19 C
Substituting the Values and Finding the Answer Now, we substitute the values into the formula:
n = 1.6 × 1 0 − 19 C 6 C = 3.75 × 1 0 19
Therefore, the number of electrons that flow through the conductor is 3.75 × 1 0 19 .
Final Answer In summary, the amount of charge that passes through the cross-section of the conductor in 30 seconds is 6 Coulombs, and the number of electrons that flow is 3.75 × 1 0 19 .
Examples
This concept is used in many real-world applications, such as calculating the amount of energy transferred in electrical circuits. For example, if you know the current flowing through a wire and the time it flows, you can calculate the total charge that has passed through the wire. This is useful in designing electrical systems and ensuring they can handle the required current and charge. Also, understanding the flow of electrons is crucial in semiconductor physics, which is the basis for modern electronics.
