A hair dryer draws a current of 9.7 A.
(a) How much charge passes through the hair dryer in 3.5 min?
1 C
(b) How many electrons does this represent?
2 electrons
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To answer both parts of the question, we need to understand the relationship between current, time, and charge.
Charge (Q) is calculated by multiplying current (I) by time (t), using the formula:
Q = I * t
(a) To determine the amount of charge passing through the hair dryer in 3.5 minutes:
Given:
Current (I) = 9.7 A
Time (t) = 3.5 min
Using the formula Q = I * t:
Q = 9.7 A * 3.5 min
Now we need to convert minutes to seconds, since the unit of current is Amperes (A), which represents the charge flowing per second. There are 60 seconds in 1 minute.
Q = 9.7 A * (3.5 min * 60 s/min)
Q = 9.7 A * 210 s
Calculating the product:
Q = 2037 C
Therefore, the amount of charge passing through the hair dryer in 3.5 minutes is 2037 Coulombs (C).
(b) To calculate the number of electrons represented by this charge:
The elementary charge (e) is the charge of a single electron, equal to approximately 1.602 x 10^-19 C.
To find the number of electrons, divide the given charge by the elementary charge:
Number of electrons = Charge / Elementary charge
Number of electrons = 2037 C / (1.602 x 10^-19 C)
Calculating the division gives us:
Number of electrons ≈ 1.271 x 10^22 electrons
Therefore, the amount of charge passing through the hair dryer represents approximately 1.271 x 10^22 electrons.
Note: In (b), the answer has been rounded to 2 significant figures for simplicity.
Y’all don’t take the time to understand it
I= Δq/Δt =N•e/ Δt.
Δq = I• Δt = 9.7•3.5•60 = ...
N = Δq/e = Δq /1.6•10^-19 = ...