A net charge of 47 mC passes through the cross-sectional area of a wire in 19.0 s.
(a) What is the current in the wire?
1 A
(b) How many electrons pass the cross-sectional area in 1.0 min?
2 electrons
I= Δq/Δt =47•10^-3/19 = ...
N = Δq/e = 47•10^-3/1.6•10^-19 = ...
To find the current in the wire, we can use Ohm's Law, which states that current (I) is equal to the charge (Q) passing through a conductor divided by the time (t) it takes for the charge to pass through it.
(a) To find the current (I), we can use the formula: I = Q / t.
Given:
Charge, Q = 47 mC (milliCoulombs)
Time, t = 19.0 s
Converting the charge from milliCoulombs to Coulombs:
Q = 47 mC = 47 x 10^(-3) C = 0.047 C
Substituting the values into the formula, we get:
I = 0.047 C / 19.0 s
Calculating the current, we find:
I = 0.0025 A
Therefore, the current in the wire is 0.0025 Amperes (or 2.5 mA).
(b) To find the number of electrons passing through the cross-sectional area in 1.0 min, we need to use the equation that relates charge (Q), current (I), and time (t).
The equation is given by: Q = I * t
We already know the current from part (a) is I = 0.0025 A. We need to convert the time from minutes to seconds since the unit of current is Amperes and time is in seconds.
1 min = 60 s
Substituting the values into the equation, we get:
Q = 0.0025 A * 60 s
Calculating the charge, we find:
Q = 0.15 C
Now, to find the number of electrons, we can use the fact that 1 Coulomb is equal to the charge of approximately 6.242 x 10^18 electrons.
Number of electrons = Q / (1.602 x 10^(-19) C)
Substituting the values, we get:
Number of electrons = 0.15 C / (1.602 x 10^(-19) C)
Calculating the number of electrons, we find:
Number of electrons ≈ 9.345 x 10^18 electrons
Therefore, approximately 9.345 x 10^18 electrons pass through the cross-sectional area in 1.0 minute.