The eyes (heating elements) of an electric range are frequently made of resistive nichrome strips. Operation of the eye is quite simple. A current is passed through the heating element causing it to dissipate power in the form of heat. Also, a four-position selector switch, shown in Fig. 2.45,

Question

The eyes (heating elements) of an electric range are frequently made of resistive nichrome strips. Operation of the eye is quite simple. A current is passed through the heating element causing it to dissipate power in the form of heat. Also, a four-position selector switch, shown in Fig. 2.45, controls the power (heat) output. In this case the eye consists of two nichrome strips modeled by the resistors [latex]R_{1}[/latex] and [latex]R_{2}[/latex] , where [latex]R_{1}[/latex] < [latex]R_{2}.[/latex]
1. How should positions A, B, C, and D be labeled with regard to high, medium, low, and off settings?
2. If we desire that high and medium correspond to 2000 W and 1200 W power dissipation, respectively, what are the values of [latex]R_{1}[/latex] and [latex]R_{2}[/latex]?
3. What is the power dissipation at the low setting?

Accepted Answer

Position A is the off setting since no current flows to the heater elements. In position B, current flows through [latex]R_{2}[/latex] only, while in position C current flows through [latex]R_{1}[/latex] only. Since [latex]R_{1}[/latex] < [latex]R_{2}[/latex], more power will be dissipated when the switch is at position C. Thus, position C is the medium setting, B is the low setting, and, by elimination, position D is the high setting.

When the switch is at the medium setting, only [latex]R_{1}[/latex] dissipates power, and we can write [latex]R_{1}[/latex] as

[latex]R_{1}\,=\,\frac{V^{2}_{S}}{P_{1}}\,=\,\frac{230^{2}}{1200}[/latex]

or

[latex]R_{1}[/latex] = 44.08 Ω

On the high setting, 2000 W of total power is delivered to [latex]R_{1}[/latex] and [latex]R_{2}[/latex]. Since [latex]R_{1}[/latex] dissipates 1200 W, [latex]R_{2}[/latex] must dissipate the remaining 800 W. Therefore, [latex]R_{2}[/latex] is

[latex]R_{2}\,=\,\frac{V^{2}_{S}}{P_{2}}\,=\,\frac{230^{2}}{800}[/latex]

or

[latex]R_{2}[/latex] = 66.13 Ω

Finally, at the low setting, only [latex]R_{2}[/latex] is connected to the voltage source; thus, the power dissipation at this setting is 800 W.

Question 2.31: The eyes (heating elements) of an electric range are frequen...

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