Question

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

(a) the current in the heating element is I=17.08 and safe for 12-gauge wire.

(b) the resistance of the dryer’s heating element at its operating temperature is R=14ohms

(c) cost per hour to operate the dryer is 45.1cent.

Step-by-step solution

definition of heating element.

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

heating element power =4.1kW

connected line voltage =240V

step 2:

(a)

current is given as,

I=$\frac{p}{v}$

Put values of P and V in I,

I$=\frac{p}{v}=\frac{4.1\times {10}^{3}W}{240V}=$17.08A

Thus, the current in the heating element is I=17.08 and safe for 12-gauge wire.

Step 3:

(b)

Power dissipated is given as,

P= $\frac{v^2}{R}$ (1)

Put all the values in equation (1),

$R=\frac{v^2}{p}=\frac{240\times 240}{4100}=14ohms$

Thus, the resistance of the dryer’s heating element at its operating temperature is R=14ohms

Step 4:

(c)

dryer costs 11 cent for energy of 1kWh.energy consumed by dryer is,

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

Cost of operating dryer is,

Cost= (11 cent) (4.1kWh) =45.1cent

Thus, cost per hour to operate the dryer is 45.1cent