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, while that of the vacuum cleaner is 5.7 A. Determine the power consumed by (a) the blow-dryer and (b) the vacuum cleaner. (c) Determine the ratio of the energy used by the blow-dryer in 17 minutes to the energy used by the vacuum cleaner in 48 minutes.

Question

Lane

Physics

15 November, 04:25

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, while that of the vacuum cleaner is 5.7 A. Determine the power consumed by (a) the blow-dryer and (b) the vacuum cleaner. (c) Determine the ratio of the energy used by the blow-dryer in 17 minutes to the energy used by the vacuum cleaner in 48 minutes.

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Answers (1)

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Janet Blair · Answer 1

Answer: See below

Explanation:

To know how much power is consumed by the two electrical object ww can use the following equation.

Power (P) = Voltage (V) * Current (A)

Where V is a constant value between the two objects (120 V) and the current, measured on amperes is equal to 12 A for the blow-dryer and the vacuum cleaner is 5.7 A. Using this equation we get the followings values.

a. For the Blow-Dryer:

Blow-Dryer's Power = Blow-Dryer's Voltage * Blow-Dryer's Current

Blow-Dryer's Power = 120 V * 12 A

Blow-Dryer's Power = 1440 Watts (W)

b. For the Vacuum Cleaner:

Vacuum Cleaner's Power = Vacuum Cleaner's Voltage * Vacuum Cleaner's Current

Vacuum Cleaner's Power = 120 V * 5.7 A

Vacuum Cleaner's Power = 684 W

Where Watts (W) is the unit for measuring power.

c. To know the energy ratio used for the blow dryer and the vaccum cleaner, we need to keep in mind that Power it the relation between Energy and time.

Watts (W) = Joules (J) / Seconds (s)

This means that one Watts thourgh a load consumes on Joules of energy per second

So we can know how much energy each device consumes by looking for the energy on the previous equation.

J = W * s

Before using this equation, we need to change the time we are given from minutes to seconds, with the following realtion

1 minute = 60 seconds

So:

17 minutes = 17 * (60 seconds) = 1020 seconds

48 minutes = 48 minutes * (60 seconds) = 2880 seconds

Using this values we can know the energy ratios:

Blow-dryer's Energy = 1440 W * 1020 s

Blow-dryer's Energy = 1468800 J

Vacuum cleaner's Energy = 684 W * 2880 s

Vacuum cleaner's Energy = 1969920 J

So that it is know the Vacuum cleaner and the Blowe-Dryer energy ratios