Question

Electrical Power

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Answer 1

This section talks about the relationship between electrical power and Ohm's Law. The following formula will be used:
\[P = IV\]
Where,
P = Power (measured in watts, also known as J/s)
I = the current (measured in amperes)
V = the voltage (measured in volts)

Note: A kilowatt is 1,000 watts.
If you see kilowatts on the test, just multiply them by 1000 to convert to watts.
\[1 kW \times \frac{ 1000 watts }{ 1 kW}\]
If you need to determine kWh (kilowatts used in an hour) simply do:
\[kW \times hours = kWh\]

Answer 2

Electrical Power - Practice

1. Your oven has a power rating of 5000 watts.
a. How many kilowatts is this?
\[5000 watts \times \frac{ 1 kW }{ 1000watts } = 5 kW\]
b. If the oven is used for 2 hours to bake cookies, how many kilowatt hours (kWh are used?)
\[5 kW \times 2 hours = 10 kWh\]
c. If you town charges $0.15/kWh, what is the cost to use the oven to bake cookies?
\[10 \times 0.15 = $1.5\]
Note: They are asking for kWh not per hour. Easy money

Answer 3

2. You use a 1200-watt hair dryer for 10 minutes each day.
a. How many minutes do you use the hair dryer in a month?
\[10minutes \times 30 days = 300\]
300 minutes per month
b. How many hours do you use the hair dryer in a month?
\[300 \div 60 = 5 hours\]
c. What is the power of the hair dryer in kilowatts?
\[1200watts \times \frac{ 1kW }{ 1000watts } = 1.2 kW\]
d. How many kilowatts-hours of electricity does the hair dryer use in a month?
\[1.2 kWh \times 5 hours = 6 kWh \]
e. If your town charges $0.15/kWh, what is the cost to use the hair dryer for a month
\[6 \times 0.15 = $0.90\]

Answer 4

3. Calculate the power rating of a home appliance (in kilowatts) that uses 8 amps of current when plugged into a 120-volt outlet.
\[P = IV\]
\[P = (8)(120) = 960 watts\]
4. Calculate the power of a motor that draws a current of 2 A when connected to a 12 volt battery.
\[P = (2)(12) = 24 watts\]
5. Your alarm clock is connected to a 120 volt circuit that draws 0.5 A of current.
a. Calculate the power of the alarm clock in watts.
\[P = (0.5)(120) = 60 watts\]
b. Convert the power to kilowatts
\[60 watts = \frac{ 1kW }{ 1000 watts } = 0.06 kW\]
c. Calculate the number of kilowatt-hours of electricity used by the alarm clock if it is left on for one year
1 year = 8760 hours
\[0.06 \times 8760 = 526.6 kWh\]
d. Calculate the cost of using the alarm clock for one year if your town charges $0.15/kWh
\[526.6 \times 0.15 = $78.84\]

Answer 5

6. Using the formula for power, calculate the amount of current through a 75-watt light bulb that is connected to a 120-volt circuit in your home.
\[P = IV\]
\[\frac{ P }{ V } = I\]
\[(I) = \frac{ 75 }{ 120 } = 0.625 A\]

Answer 6

7. The following questions refer to the above diagram
a. What is the total voltage of the circuit?
\[V_{total} = 1.5 + 1.5 = 3 V\]
b. What is the current in the circuit?
\[(I) = \frac{ 3 }{ 3 } = 1 A\]
c. What is the power of the light bulb?
\[P = (1)(3) = 1 watt\]
8. A toaster is plugged into a 120-volt housed circuit. It draws 5 amps of current.
a. What is the resistance of the toaster?
\[R = \frac{ V }{ I }\]
\[R = \frac{ 120 }{ 5 } = 24 \Omega\]
b. What is the power of the toaster in watts?
\[P = IV\]
\[P = (5)(120) = 600 watts\]
c. What is the power in kilowatts?
\[600 watts \times \frac{ 1kW }{ 1000 watts } = 0.6 kW\]
9. A clothes dryer in a home has a power of 4,500 watts and runs on a special 220-volt household circuit.
a. What is the current through the dryer?
\[(I) = \frac{ P }{ V }\]
\[(I) = \frac{ 4,500 watts }{ 220 V } = 20.5 A\]
b. What is the resistance of the dryer?
\[R = \frac{ V }{ I }\]
\[R = \frac{ 220 }{ 20.5 } = 10.8 \Omega\]
c. How many kilowatt-hours of electricity are used by the dryer if it is used for 4 hours in one week?
\[4,500 watts \times \frac{ 1 kW }{ 1000watts} = 4.5 kW\]
\[4.5 kW \times 4 hours = 18 kWh\]
d. How much does it cost to run the dryer for one year if it is used for 4 hours each week at a cost of $0.15/kWh?
\[18 \times 0.15 = $2.7\]

Answer 7

10. A circuit contains a 12-volt battery and two 3-ohms bulbs in series.
a. Calculate the total resistance of the circuit
\[R_{total} = 3 + 3 = 6 \Omega\]
b. Calculate the total current of the circuit.
\[(I) = \frac{ 12 }{ 6 } = 2A\]
c. Calculate the power of each bulb
\[V = (2)(3) = 6 V\]
\[P = (2)(6) = 12 watts\]
d. Calculate the power supplied by the battery
\[P = (2)(12) = 24 watts\]

Answer 8

11. A circuit contains a 12-volt battery and two 3-ohm bulbs in parallel.
a. What is the voltage across each branch
\[V_{3} = V_{3} = V_{batt} = 12 V\]
Voltage same across all branches in a parallel circuit.
b. Calculate the current in each branch
\[I_{3} = \frac{ 12 }{ 3 } = 4 A\]
Answer for both since they both have a resistance of three.
c. Calculate the power of each bulb.
\[P = (4)(12) = 48 watts\]
d. Calculate the total current in the circuit.
\[I_{total} = 4 + 4 = 8A\]
e. Calculate the power supplied by the battery.
\[P = (8)(12) = 96 watts\]