Question

A blow-dryer and a vacuum cleaner each operate with a voltage of 120 V. The current rating of the blow-dryer is 9.2 A, while that of the vacuum cleaner is 5.9 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 18 minutes to the energy used by the vacuum cleaner in 56 minutes.

Answer 1

(a) Determine the power consumed by the blow-dryer.

P = V*I

where P is the power consumed, V is the voltage applied and I is the current passing through blow-dryer.

now putting the values of V= 120 v, I = 9.2 A

P = 120 * 9.2 watt

P = 1104 watt

(b)

Determine the power consumed by the vaccum cleaner.

P = V*I

where P is the power consumed, V is the voltage applied and I is the current passing through vaccum cleaner.

now putting the values of V= 120 v, I = 5.9 A

p = 120 * 5.9 watt

p = 708 watt

(c)

The relationship between power and energy is,

P = E / t

E = P * t

Therefore, the ratio of the energy used by the blow-dryer(E) to the energy used by the vacuum(e) is

E/e = (P * t1)/(p * t2)

E/e = ( 1104 * 18 * 60) / (708 * 56 * 60)

E/e = (1104 * 9)/(708 * 28)

E/e = 9936 / 19824

E/e = 0.5012

thus, the ratio of the energy used by the blow dryer in 18 minutes to the energy used by vaccum cleaner in 56 minutes is approx 0.5 or 1/2.