To find the average current in the power line, we can use the formula for electrical power:

$P = VI$

Where:

• $P$ is the power (in watts, W),
• $V$ is the voltage (in volts, V),
• $I$ is the current (in amperes, A).

However, the energy consumption is given in kilowatt-hours (kWh), not watts. So, we first convert the energy usage to total power over time and then calculate the average current.

Step 1: Convert kWh to Watts

The family uses 860 kWh per month. We convert that to watts by recalling that:

$1 \text{ kWh} = 1000 \text{ W} \times 1 \text{ hour}$

So, the total energy consumption is:

$860 \text{ kWh} = 860 \times 1000 \text{ Wh} = 860,000 \text{ Wh}$

Step 2: Determine the Average Power Consumption

Since 1 month has approximately 30 days, and each day has 24 hours, the total time is:

$T = 30 \times 24 = 720 \text{ hours}$

Now, the average power consumption $P$ is the total energy divided by the time:

$P = \frac{860,000 \text{ Wh}}{720 \text{ hours}} = 1194.44 \text{ W}$

Step 3: Calculate the Average Current

Now, using the power equation $P = VI$, we can solve for the current $I$:

$I = \frac{P}{V} = \frac{1194.44 \text{ W}}{100 \text{ V}} = 11.94 \text{ A}$

Thus, the average current in the power line is approximately:

$I = 11.94 \text{ A}$

Conclusion:

The average current flowing through the 100 V power line to the house is 11.94 A.

---

Would you like further details or have any questions? Here are five related questions to expand on this topic:

1. How would the current change if the voltage were increased to 120 V?
2. How is electrical energy measured and billed in a household?
3. What factors can affect the power consumption of a household?
4. What is the difference between alternating current (AC) and direct current (DC)?
5. How do you convert electrical power from watts to kilowatts?

Tip: Keeping energy-efficient appliances can significantly reduce your monthly kWh consumption.