A blow-dryer and a vacuum cleaner each operate with a voltage of 120 V. The current rating of the blow-dryer is 12 A, and that of the vacuum cleaner is 5.5 A.
Determine the power consumed by the blow-dryer.
Determine the power consumed by the vacuum cleaner.
Determine the ratio of the energy used by the blow-dryer in 19 minutes to the energy used by the vacuum cleaner in one-half hour.
Ebd / Evc =
the first two parts i got but the last im not sure what to do.
The energy consumption ratio is the product of the time interval ratio and the power (or current) ratio.
The current ratio is
Pbd/Pvc = 12/5.5
The energy ratio is
Ebd / Evc =
Pbd/Pvc * Tbd/Tvc = (12/5.5)*(19/30)
= 1.382
Well, let's tackle the last part together! To determine the ratio of the energy used by the blow-dryer in 19 minutes to the energy used by the vacuum cleaner in one-half hour, we need to calculate the energy used by each device.
The formula for energy (E) is given by:
Energy = Power x Time
First, let's find the power consumed by the blow-dryer:
Power = Voltage x Current
Power = 120 V x 12 A
Power = 1440 W
Next, let's find the power consumed by the vacuum cleaner:
Power = Voltage x Current
Power = 120 V x 5.5 A
Power = 660 W
Now, let's calculate the energy used by the blow-dryer in 19 minutes:
Energy used by blow-dryer = Power x Time
Energy used by blow-dryer = 1440 W x (19 minutes / 60 minutes)
Energy used by blow-dryer = 1440 W x 0.3167
Energy used by blow-dryer = 455.28 Wh (watt-hours)
Lastly, let's calculate the energy used by the vacuum cleaner in one-half hour:
Energy used by vacuum cleaner = Power x Time
Energy used by vacuum cleaner = 660 W x (30 minutes / 60 minutes)
Energy used by vacuum cleaner = 660 W x 0.5
Energy used by vacuum cleaner = 330 Wh (watt-hours)
Now, we can find the ratio of the energy used by the blow-dryer to the energy used by the vacuum cleaner:
Ratio = Energy used by blow-dryer / Energy used by vacuum cleaner
Ratio = 455.28 Wh / 330 Wh
Ratio ≈ 1.38
Therefore, the ratio of the energy used by the blow-dryer in 19 minutes to the energy used by the vacuum cleaner in one-half hour is approximately Ebd / Evc = 1.38.
To determine the power consumed by the blow-dryer, you can use the formula:
Power (P) = Voltage (V) x Current (I)
Therefore, the power consumed by the blow-dryer can be calculated as:
P (blow-dryer) = 120 V x 12 A
P (blow-dryer) = 1440 W
Similarly, to determine the power consumed by the vacuum cleaner, you can use the same formula:
P (vacuum cleaner) = 120 V x 5.5 A
P (vacuum cleaner) = 660 W
Now, to determine the ratio of the energy used by the blow-dryer in 19 minutes to the energy used by the vacuum cleaner in one-half hour, you need to calculate the energy used by each appliance and then compare them.
Energy (E) can be calculated using the formula:
Energy (E) = Power (P) x Time (t)
Energy used by blow-dryer in 19 minutes:
E (blow-dryer) = P (blow-dryer) x t (blow-dryer)
E (blow-dryer) = 1440 W x (19/60) h (convert minutes to hours)
Energy used by vacuum cleaner in one-half hour:
E (vacuum cleaner) = P (vacuum cleaner) x t (vacuum cleaner)
E (vacuum cleaner) = 660 W x (0.5) h (30 minutes is half of an hour)
Finally, you can calculate the ratio of E (blow-dryer) to E (vacuum cleaner):
Ebd / Evc = E (blow-dryer) / E (vacuum cleaner)
Substituting the calculated values in the formula will give you the desired result.
To determine the power consumed by the blow-dryer and the vacuum cleaner, you can use the formula:
Power (P) = Voltage (V) × Current (I)
For the blow-dryer:
Power (Pbd) = 120 V × 12 A = 1440 watts
For the vacuum cleaner:
Power (Pvc) = 120 V × 5.5 A = 660 watts
Now, to determine the ratio of the energy used by the blow-dryer in 19 minutes to the energy used by the vacuum cleaner in one-half hour, you need to calculate the energy consumed by each appliance.
The formula to calculate energy is:
Energy (E) = Power (P) × Time (t)
For the blow-dryer:
Energy used by the blow-dryer (Ebd) = Pbd × tbd
Given that tbd = 19 minutes, you can convert it to hours by dividing by 60:
tbd = 19 minutes ÷ 60 = 0.3167 hours
So, you can calculate the energy used by the blow-dryer:
Ebd = Pbd × tbd = 1440 watts × 0.3167 hours
For the vacuum cleaner:
Energy used by the vacuum cleaner (Evc) = Pvc × tvc
Given that tvc = one-half hour = 0.5 hours, you can calculate the energy used by the vacuum cleaner:
Evc = Pvc × tvc = 660 watts × 0.5 hours
Finally, to determine the ratio of Ebd to Evc:
Ebd / Evc = (1440 watts × 0.3167 hours) / (660 watts × 0.5 hours)
Simplifying this expression will give you the desired ratio.