91Ó°ÊÓ

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

Heating element power $\mathrm{P}=4.1\mathrm{kW}\left(\frac{{10}^3\mathrm{W}}{1\mathrm{kW}}\right)=4.1×{10}^3\mathrm{W}$

Connected line voltage = 240 V

(a)

The current is given as,

$\mathrm{I}=\frac{\mathrm{P}}{\mathrm{V}}$…â¶Ä¦â¶Ä¦â¶Ä¦â¶Ä¦â¶Ä¦.(1)

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

$$\begin{gathered} \mathrm{I}=\frac{4.1×{10}^3\mathrm{W}}{240\mathrm{V}} \\ =17.08\mathrm{A} \\ \mathrm{Thus},\mathrm{the}\mathrm{current}\mathrm{in}\mathrm{the}\mathrm{heating}\mathrm{element}\mathrm{is}\mathrm{I}=17.08\mathrm{A}\mathrm{which}\mathrm{is}\mathrm{safe}\mathrm{for}12-\mathrm{gauge}\mathrm{wire}. \end{gathered}$$

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

(b)

The power dissipated is given as,

$\mathrm{P}=\frac{{\mathrm{V}}^2\mathrm{R}}{}$ (2)

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

$$\begin{gathered} \mathrm{R}=\frac{{\left(250\mathrm{V}\right)}^2}{4.1×{10}^3\mathrm{W}} \\ =14.1\mathrm{Î\copyright } \end{gathered}$$

Thus, the resistance of the dryer’s heating element at its operating temperature is$14.1\mathrm{Î\copyright }$

(c)

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

$\mathrm{E}=\mathrm{P}×\mathrm{t}$

E=$4.1\mathrm{kW}×1\mathrm{hE}=\mathrm{pt}.$pt.=(4.1kW) (1h) =4.1kWh

$\mathrm{E}=4.1\mathrm{kWh}$

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

$$\begin{gathered} \mathrm{Operating}\mathrm{cost}=4.1\mathrm{kWh}×11\mathrm{cent}/\mathrm{kWh} \\ =45.1\mathrm{cent} \end{gathered}$$

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