Question

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.

Answer 1

(a) P₁ = 1320 W

(b) P₂ = 480 W

(c)
`(E_1)/(E_2) = 0.46`

Step-by-step explanation:

(a)

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

`P_1 = VI`

where,

P₁ = Power Consumed by the blow dryer = ?

V = Voltage = 120 V

I = Current Rating of the blow dryer = 11 A

Therefore,

`P_1 = (120\ V)(11\ A)\\`

P₁ = 1320 W

(b)

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

`P_2 = VI`

where,

P₂ = Power Consumed by the vacuum cleaner = ?

V = Voltage = 120 V

I = Current Rating of the vacuum cleaner = 4 A

Therefore,

`P_2 = (120\ V)(4\ A)\\`

P₂ = 480 W

(c)

`(E_1)/(E_2) = (P_1t_1)/(P_2t_2)`

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,

`(E_1)/(E_2) = ((1320\ W)(900\ s))/((480\ W)(5400\ s))\\\\(E_1)/(E_2) = 0.46`