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The heating element of an electric dryer is rated at 4.1 kW when connected to a 240-V line. (a) What is the current in the heating element? Is 12-gauge wire large enough to supply this current? (b) What is the resistance of the dryer’s heating element at its operating temperature? (c) At 11 cents per kWh, how much does it cost per hour to operate the dryer?

Short Answer

Expert verified

(a) The current in the heating element is1=17.08A and safe for 12-gauge wire.

(b) The resistance of the dryer’s heating element at its operating temperature is14.1Ω

(c) Cost per hour to operate the dryer is 45.1 Cents.

Step by step solution

01

Definition of the heating element.

The heating element is part of an electric heating appliance in which electric energy is transformed into heat.

Heating element power P=4.1kW103W1kW=4.1×103W

Connected line voltage = 240 V

02

Calculation of current

(a)

The current is given as,

I=PV……………….(1)

Substitute the values of P and V in equation (1) to get the current,

I=4.1×103W240V=17.08AThus,thecurrentintheheatingelementisI=17.08Awhichissafefor12-gaugewire.

Thus, the current in the heating element is which is safe for 12-gauge wire.

03

Step 3:

(b)

The power dissipated is given as,

P=V2R (2)

Substitute all the values in equation (2) which gives resistance,

R=250V24.1×103W=14.1Ω

Thus, the resistance of the dryer’s heating element at its operating temperature is14.1Ω

04

Step 4:

(c)

The dryer costs 11 cents for the energy of 1 kWh.energy consumed by the dryer is,

E=P×t

E=4.1kW×1hE=pt.pt.=(4.1kW) (1h) =4.1kWh

E=4.1kWh

The cost of operating the dryer for 1 h can be calculated as,

Operatingcost=4.1kWh×11cent/kWh=45.1cent

Thus, the cost per hour to operate the dryer is 45.1 Cents.

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