Question

For the scenario in the previous question, how many electrons moved through the circuit?

a) 2.5 × 10²0 electrons
b) 1.4 × 10²4 electrons
c) 1.5 × 10²3 electrons
d) 1.75 × 10²2 electrons

Answer 1

To find the number of electrons that moved through the circuit, we use the equation number of electrons = total charge / charge per electron. We find the total charge by multiplying the current in the circuit by the time the current flows. Then, we divide the total charge by the charge per electron to find the number of electrons.

Step-by-step explanation:

To find the number of electrons that moved through the circuit, we will use the equation:

Number of electrons = total charge / charge per electron

In the given scenario, we are not given the total charge directly, but we are given the current in the circuit. The current (I) is given by the equation:

I = Q / t

where I is the current, Q is the charge, and t is the time. Rearranging the equation, we get:

Q = I * t

Now we can find the total charge:

Q = 2.5 A * 35 minutes

Converting minutes to seconds:

Q = 2.5 A * 35 minutes * 60 seconds/minute

Q = 5250 C

Now, we can find the number of electrons:

Number of electrons = 5250 C / (1.6 x 10^-19 C/electron)

Number of electrons = 3.28 x 10^22 electrons

Answer 2

The electrons moved through the circuit are (b) 1.4 × 10²⁴ electrons.

Step-by-step explanation:

To determine the number of electrons that moved through the circuit, we can use the formula:

`\[ Q = I \cdot t \]`

where:

Q is the charge (in coulombs),

I is the current (in amperes),

t is the time (in seconds).

Since 1 Coulomb is equivalent to the charge of approximately
`\( 6.242 * 10^(18) \)` electrons, the number of electrons (N) can be calculated as:

`\[ N = (Q)/(e) \]`

where e is the elementary charge (
`\( 1.6 * 10^(-19) \) C`).

Given that I = 5.0 A and t = 2.8 hours, first convert the time to seconds: 2.8 hours
`\( * 60 \) minutes/hour \( * 60 \)` seconds/minute. Then, use the formula to find Q, and finally, calculate N.

`\[ Q = 5.0 \, \text{A} * (2.8 \, \text{hours} * 60`,

`\text{minutes/hour} * 60 \, \text{seconds/minute}) \]`

`\[ N = (Q)/(e) \]`

After the calculation, the number of electrons (N) is approximately
`\( 1.4 * 10^(24) \)`. Therefore, option (b) is the correct answer. This calculation illustrates the relationship between current, time, and the quantity of charge, allowing us to determine the number of electrons passing through the circuit during the specified time interval.