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A blow-dryer and a vacuum cleaner each operate with a voltage of 120 V. The current rating of the blow-dryer is 11 A, and that of the vacuum cleaner is 4.0 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 15 minutes to the energy used by the vacuum cleaner in one- half hour.

Sagot :

Answer:

(a) P₁ = 1320 W

(b) P₂ = 480 W

(c) [tex]\frac{E_1}{E_2} = 0.46[/tex]

Explanation:

(a)

The power consumed by the blow dryer can be calculated as follows:

[tex]P_1 = VI[/tex]

where,

P₁ = Power Consumed by the blow dryer = ?

V = Voltage = 120 V

I = Current Rating of the blow dryer = 11 A

Therefore,

[tex]P_1 = (120\ V)(11\ A)\\[/tex]

P₁ = 1320 W

(b)

The power consumed by the blow dryer can be calculated as follows:

[tex]P_2 = VI[/tex]

where,

P₂ = Power Consumed by the vacuum cleaner = ?

V = Voltage = 120 V

I = Current Rating of the vacuum cleaner = 4 A

Therefore,

[tex]P_2 = (120\ V)(4\ A)\\[/tex]

P₂ = 480 W

(c)

[tex]\frac{E_1}{E_2} = \frac{P_1t_1}{P_2t_2}[/tex]

where,

E₁ = Energy used by the blow-dryer

E₂ = Energy used by the vacuum cleaner

t₁ = time of use of the blow-dryer = (15 min)(60 s/1 min) = 900 s

t₂ = time of use of the vacuum cleaner = (1.5 h)(3600 s/1 h) = 5400 s

Therefore,

[tex]\frac{E_1}{E_2} = \frac{(1320\ W)(900\ s)}{(480\ W)(5400\ s)}\\\\\frac{E_1}{E_2} = 0.46[/tex]