3. A central air conditioner in a typical American home operates on a 220V circuit (higher voltage than the standard 120V wired throughout the house) and uses 20A of current. a. How much power is used when it is running? b. Why is it wired to run off 220 V instead of 120 V? c. PEPCO (the electrical utility in Md) charges 15 cents/ kWh for electricity. If the AC is running for 6 hours per day, how much will I spend on electricity ner summer month?

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Chapter1: Units, Trigonometry. And Vectors
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**Title: Understanding Central Air Conditioner Power Consumption**

**Introduction:**
This exercise explores the power consumption of a central air conditioner in a typical American home. We'll analyze its operation on a 220V circuit, in contrast to the standard 120V wiring found throughout the house, and understand the implications for electricity usage and cost.

**Scenario:**
A central air conditioner operates on a 220V circuit and uses 20A of current.

**Questions:**

**a. How much power is used when it is running?**

To calculate the power consumption (in watts), use the formula:  
\[ \text{Power (P)} = \text{Voltage (V)} \times \text{Current (I)} \]

**b. Why is it wired to run off 220 V instead of 120 V?**

Explore the benefits of using a higher voltage for large appliances, such as increased efficiency, reduced current draw, and decreased heat loss in wiring.

**c. Cost Analysis:**

PEPCO (the electrical utility in Maryland) charges 15 cents per kilowatt-hour (kWh) for electricity. If the air conditioner runs for 6 hours per day, calculate the monthly cost of operation (assuming a 30-day month). Use the power consumption calculated in part (a) to determine the total kWh used.

**Conclusion:**
Understanding the power usage and cost implications of running a central air conditioner helps in making informed decisions about energy use and budgeting for utility bills.
Transcribed Image Text:**Title: Understanding Central Air Conditioner Power Consumption** **Introduction:** This exercise explores the power consumption of a central air conditioner in a typical American home. We'll analyze its operation on a 220V circuit, in contrast to the standard 120V wiring found throughout the house, and understand the implications for electricity usage and cost. **Scenario:** A central air conditioner operates on a 220V circuit and uses 20A of current. **Questions:** **a. How much power is used when it is running?** To calculate the power consumption (in watts), use the formula: \[ \text{Power (P)} = \text{Voltage (V)} \times \text{Current (I)} \] **b. Why is it wired to run off 220 V instead of 120 V?** Explore the benefits of using a higher voltage for large appliances, such as increased efficiency, reduced current draw, and decreased heat loss in wiring. **c. Cost Analysis:** PEPCO (the electrical utility in Maryland) charges 15 cents per kilowatt-hour (kWh) for electricity. If the air conditioner runs for 6 hours per day, calculate the monthly cost of operation (assuming a 30-day month). Use the power consumption calculated in part (a) to determine the total kWh used. **Conclusion:** Understanding the power usage and cost implications of running a central air conditioner helps in making informed decisions about energy use and budgeting for utility bills.
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