during the 4.0 min a 5.0a current is set up in a wire, how many (a) coulombs and (b) electrons pass through any given point in the wire?
To determine the number of coulombs and electrons that pass through any given point in the wire, we need to use the formula:
Q = I × t
Where:
Q is the charge in coulombs (C),
I is the current in amperes (A), and
t is the time in seconds (s).
(a) Coulombs:
Given that the current is 5.0A and the time is 4.0 minutes (which is 240 seconds), we can substitute these values into the formula:
Q = (5.0A) × (240s)
Q = 1200C
Therefore, during the 4.0 minutes, a total charge of 1200 coulombs passes through any given point in the wire.
(b) Electrons:
To calculate the number of electrons, we need to use the relation between charge and the elementary charge (e). One coulomb is equivalent to approximately 6.242 × 10^18 elementary charges.
Number of electrons = Q / e
Using the value of Q we calculated earlier (1200C), we can determine the number of electrons:
Number of electrons = (1200C) / (6.242 × 10^18 elementary charges)
You can simplify this value further to get the exact number of electrons that pass through any given point in the wire during the 4.0-minute period.
To determine the number of coulombs and electrons that pass through any given point in the wire, we can use the formula:
Q = I * t
where:
Q is the charge in coulombs (C),
I is the current in amperes (A),
t is the time in seconds (s).
(a) Coulombs:
Given that the current is 5.0 A and the time is 4.0 min (convert it to seconds):
t = 4.0 min * 60 s/min = 240 s
Now, we can calculate the charge (Q):
Q = 5.0 A * 240 s = 1200 C
Therefore, (a) 1200 coulombs pass through any given point in the wire.
(b) Electrons:
To find the number of electrons, we need to know the charge of a single electron.
The elementary charge of an electron is approximately 1.6 x 10^-19 C.
So, we can divide the charge in coulombs (Q) by the charge of a single electron to get the number of electrons:
Number of electrons = Q / (1.6 x 10^-19 C)
Number of electrons = 1200 C / (1.6 x 10^-19 C)
Number of electrons ≈ 7.5 x 10^21 electrons.
Therefore, (b) approximately 7.5 x 10^21 electrons pass through any given point in the wire.