A typical American family uses 860 kWh of electricity a month.
What is the average current in the 100 V power line to the house?

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.

A typical American family uses 860 kWh of electricity a month. What is the average current in the 100 V power line to the house?

Learn how to calculate the average current for a household consuming 860 kWh per month with a 100 V power line. This solution involves key electrical concepts such as power, energy, and current, using the formula P = VI to determine the current. Suitable for high school students in Grades 9-12.

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