If a 1.61 A current flows through the leads of an electrical appliance, how many electrons per second pass through it?
The correct answer and explanation is:
To find the number of electrons passing through the appliance, we need to use the relationship between current and charge flow. The current (II) is defined as the rate at which charge flows, and is given by: I=QtI = \frac{Q}{t}
Where:
- II is the current in amperes (A),
- QQ is the charge in coulombs (C),
- tt is the time in seconds (s).
- Charge of an Electron:
Each electron carries a fundamental charge of approximately 1.6×10−191.6 \times 10^{-19} coulombs. - Total Charge per Second (Coulombs per Second):
In the case of a 1.61 A current, we can calculate how much charge flows per second:
I=Qt ⟹ Q=I×tI = \frac{Q}{t} \implies Q = I \times t
For I=1.61 AI = 1.61 \, A and t=1 st = 1 \, \text{s}, we find that: Q=1.61 CQ = 1.61 \, C
This means that in 1 second, 1.61 coulombs of charge pass through the appliance.
- Number of Electrons Passing Through:
Now, to find the number of electrons, we use the fact that each electron carries 1.6×10−191.6 \times 10^{-19} coulombs of charge. The number of electrons (NN) passing through can be calculated as:
N=QeN = \frac{Q}{e}
Where:
- Q=1.61 CQ = 1.61 \, C,
- e=1.6×10−19 Ce = 1.6 \times 10^{-19} \, C.
Substitute the values: N=1.61 C1.6×10−19 CN = \frac{1.61 \, C}{1.6 \times 10^{-19} \, C} N=1.00625×1019 electronsN = 1.00625 \times 10^{19} \text{ electrons}
Thus, approximately 1.01×10191.01 \times 10^{19} electrons pass through the appliance every second when a 1.61 A current flows through it.
Explanation:
The calculation illustrates how electrical current, which is the flow of charge, is related to the number of electrons passing through a conductor. A current of 1.61 A means that 1.61 coulombs of charge move through the circuit every second. Since each electron has a specific charge, dividing the total charge by the electron’s charge gives us the number of electrons passing through.