1. A typical household circuit is capable of carrying 15.0 Amps of current at 120 V before the circuit breaker will trip. How many 1500-W hair dryers can run off one such circuit?
In the rush to get ready for lecture, a physics professor leaves the hair dryer described in the previous problem running and does not turn it off until he gets home 6.3 hours later. How much will this add, in dollars, to his next electric bill (assume electricity costs $0.078 per kilowatt-hr)?
1. P = E*I = 120 * 15 = 1800 W.
1800/1500 = 1.2 or 1 Dryer.
2. 1500W. = 1.5kW.
Cost = 1.5 * 6.3 * 0.078 =
Well, let's do some math!
If a typical household circuit can carry 15.0 Amps of current, we can divide the total current by the current used by each hairdryer:
15.0 Amps / 1500 Watts = 10 hairdryers
So, the professor can run up to 10 hairdryers on one circuit without causing the circuit breaker to trip. Imagine the fabulous hairstyles he could achieve!
Now, we need to calculate the amount of energy the hairdryer will use in 6.3 hours. Since a hairdryer uses 1500 Watts, we can convert this to kilowatts:
1500 Watts / 1000 = 1.5 kilowatts
Next, we multiply the power (1.5 kilowatts) by the time (6.3 hours):
1.5 kilowatts x 6.3 hours = 9.45 kilowatt-hours
Finally, we multiply the energy consumed (9.45 kilowatt-hours) by the cost per kilowatt-hour ($0.078):
9.45 kilowatt-hours x $0.078/kWh = $0.7359
So, leaving the hairdryer running for 6.3 hours would add approximately $0.7359 to the professor's next electric bill. Looks like he'll have to teach an extra class or two to cover that expense!
To determine how many 1500-W hair dryers can run off one circuit, we need to calculate the total power consumed by one hair dryer and then divide the maximum power the circuit can handle by the power consumed by one hair dryer.
Step 1: Calculate the power consumed by one hair dryer:
Power consumed = 1500 W
Step 2: Calculate the maximum power the circuit can handle:
Maximum power = 15.0 A * 120 V
Step 3: Divide the maximum power by the power consumed by one hair dryer:
Number of hair dryers = Maximum power / Power consumed by one hair dryer
Number of hair dryers = (15.0 A * 120 V) / 1500 W
Number of hair dryers = 1.2 hair dryers
Since we can't have a fraction of a hair dryer, we can conclude that only 1 hair dryer can run off this circuit.
To calculate how much this will add to the professor's electric bill, we need to determine the energy consumption of the hair dryer during the 6.3 hours it was running.
Step 1: Calculate the energy consumption of one hair dryer per hour:
Energy consumed = Power consumed * time
Energy consumed = 1500 W * 1 hour
Step 2: Calculate the energy consumed by one hair dryer in 6.3 hours:
Total energy consumed = Energy consumed per hour * 6.3 hours
Total energy consumed = 1500 W * 6.3 hours
Step 3: Convert the energy consumed into kilowatt-hours (kWh):
Total energy consumed in kWh = Total energy consumed / 1000
Step 4: Calculate the cost:
Cost = Total energy consumed in kWh * Cost per kWh
Cost = (1500 W * 6.3 hours) / 1000 * $0.078
Therefore, running the hair dryer for 6.3 hours will add $7.37 to the professor's next electric bill.
To figure out how many hair dryers can run off one circuit, we need to first calculate the current drawn by each hair dryer and then determine the maximum number that can be connected.
1. Step 1: Calculate the current drawn by each hair dryer.
We are given that the circuit can carry a current of 15.0 Amps. Each hair dryer draws 1500 Watts of power. Since power is equal to voltage multiplied by current (P = V * I), we can rearrange the formula to calculate the current drawn by each hair dryer:
I = P / V,
where I is the current, P is the power, and V is the voltage.
Substituting the given values, we find that each hair dryer draws:
I = 1500 W / 120 V = 12.5 Amps.
2. Step 2: Determine the maximum number of hair dryers that can be connected to the circuit.
To determine the maximum number of hair dryers, we divide the maximum current capacity of the circuit (15.0 Amps) by the current drawn by each hair dryer (12.5 Amps):
Maximum number of hair dryers = 15.0 Amps / 12.5 Amps ≈ 1.2.
Therefore, only one hair dryer can be connected to this circuit.
To calculate how much the professor's electric bill will increase when leaving the hair dryer on for 6.3 hours, we can use the power consumption and the cost of electricity.
3. Step 3: Calculate the energy consumed by the hair dryer.
The energy consumed by an electrical device can be calculated using the formula:
Energy (in kilowatt-hours) = Power (in kilowatts) * Time (in hours).
Since the power consumption of the hair dryer is given in watts, we need to convert it to kilowatts:
Power (in kilowatts) = Power (in watts) / 1000.
Substituting the given values, we find:
Power (in kilowatts) = 1500 W / 1000 = 1.5 kW.
Now we can calculate the energy consumed by the hair dryer:
Energy (in kilowatt-hours) = 1.5 kW * 6.3 hours = 9.45 kWh.
4. Step 4: Calculate the cost of the energy consumed.
To calculate the cost, we need to multiply the energy consumed by the cost of electricity per kilowatt-hour:
Cost = Energy (in kilowatt-hours) * Cost per kilowatt-hour.
Substituting the given cost per kilowatt-hour ($0.078) and the energy consumed (9.45 kWh), we find:
Cost = 9.45 kWh * $0.078/kWh = $0.7371.
Therefore, leaving the hair dryer on for 6.3 hours will add approximately $0.7371 to the professor's next electric bill.