A blow-dryer and a vacuum cleaner each operate with a voltage of 120 V. The current rating of the blow-dryer is 14 A, while that of the vacuum cleaner is 4.2 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 16 minutes to the energy used by the vacuum cleaner in 43 minutes.

Respuesta :

Answer:

The correct solution is:

(a) 1680 W

(b) 504 W

(c) 1.240

Explanation:

The given values are:

Voltage,

V = 120 V

Current of blow dryer,

I₁ = 14 A

Current of vacuum cleaner,

I₂ = 4.2 A

Time,

t₁ = 16 min

t₂ = 43 min

As we know,

⇒ [tex]Power (P) = VI[/tex]

(a)

For blow dryer:

⇒ [tex]P_1=V\times I_1[/tex]

        [tex]=120\times 14[/tex]

        [tex]=1680 \ W[/tex]

(b)

For Vacuum cleaner:

⇒ [tex]P_2=V\times I_2[/tex]

        [tex]=120\times 4.2[/tex]

        [tex]=504 \ W[/tex]

(c)

The ratio will be:

= [tex]\frac{Blow \ dryer \ energy}{Vacuum \ cleaner \ energy}[/tex]

= [tex]\frac{P_1\times t_1}{P_1\times t_2}[/tex]

= [tex]\frac{1680\times 16}{504\times 43}[/tex]

= [tex]\frac{26880}{21672}[/tex]

= [tex]1.240[/tex]