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.
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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 โ 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) ร Current (I)
For the blow-dryer:
Power (Pbd) = 120 V ร 12 A = 1440 watts
For the vacuum cleaner:
Power (Pvc) = 120 V ร 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) ร Time (t)
For the blow-dryer:
Energy used by the blow-dryer (Ebd) = Pbd ร tbd
Given that tbd = 19 minutes, you can convert it to hours by dividing by 60:
tbd = 19 minutes รท 60 = 0.3167 hours
So, you can calculate the energy used by the blow-dryer:
Ebd = Pbd ร tbd = 1440 watts ร 0.3167 hours
For the vacuum cleaner:
Energy used by the vacuum cleaner (Evc) = Pvc ร tvc
Given that tvc = one-half hour = 0.5 hours, you can calculate the energy used by the vacuum cleaner:
Evc = Pvc ร tvc = 660 watts ร 0.5 hours
Finally, to determine the ratio of Ebd to Evc:
Ebd / Evc = (1440 watts ร 0.3167 hours) / (660 watts ร 0.5 hours)
Simplifying this expression will give you the desired ratio.