To solve this problem, let’s go through it step by step.

Given:

• Power of the light bulb, $P = 8 \, \text{W}$
• Voltage of the circuit, $V = 230 \, \text{V}$
• Time, $t = 1 \, \text{hour} = 3600 \, \text{s}$

Goal:

Calculate the number of electrons passing through a point in the circuit in one hour.

Solution:

1. Calculate the Current (I)

   The power formula in terms of current and voltage is: $P = IV$ Rearranging for current $I$: $I = \frac{P}{V}$ Substitute the given values: $I = \frac{8}{230} = 0.0348 \, \text{A} \, (\text{approximately})$

2. Calculate the Total Charge (Q)

   Using the formula for current $I = \frac{Q}{t}$, where $Q$ is the charge and $t$ is the time: $Q = It$ Substitute $I = 0.0348 \, \text{A}$ and $t = 3600 \, \text{s}$: $Q = 0.0348 \times 3600 = 125.28 \, \text{C}$

3. Calculate the Number of Electrons

   The charge of a single electron $e$ is approximately $1.6 \times 10^{-19} \, \text{C}$.

   The number of electrons $n$ can be found by: $n = \frac{Q}{e}$ Substitute $Q = 125.28 \, \text{C}$ and $e = 1.6 \times 10^{-19} \, \text{C}$: $n = \frac{125.28}{1.6 \times 10^{-19}} = 7.83 \times 10^{20} \, \text{electrons}$

Answer:

The number of electrons passing through a point in the circuit in one hour is approximately $7.83 \times 10^{20}$.

Would you like more details on any step, or do you have any questions?

Here are some related questions to explore further:

1. How is electric current related to the flow of electrons?
2. What is the significance of power in an electrical circuit?
3. How does voltage affect the current in a circuit?
4. Why is the charge of an electron so small?
5. What would change in the calculation if the power of the bulb were different?

Tip: Remember, power (watts) divided by voltage (volts) gives the current (amperes) directly, which is very helpful in solving these types of problems.