Question

The analogy between electrical and thermal systems can be used to analyze the behavior of a pot heating on an electric stove. The heating element is modeled as shown in Figure P4.54. Find the "heat capacity" of the burner, $C_S$, if the burner reaches 90 percent of the desired temperature in 10 s . Assume $R_S=1.5 \Omega$. (FIGURE CAN'T COPY) Figure P4.54

   The analogy between electrical and thermal systems can be used to analyze the behavior of a pot heating on an electric stove. The heating element is modeled as shown in Figure P4.54. Find the "heat capacity" of the burner, $C_S$, if the burner reaches 90 percent of the desired temperature in 10 s . Assume $R_S=1.5 \Omega$.
(FIGURE CAN'T COPY)
Figure P4.54
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Principles and Applications of Electrical Engineering
Principles and Applications of Electrical Engineering
Giorgio Rizzoni,… 7th Edition
Chapter 4, Problem 54 ↓
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The analogy between electrical and thermal systems can be used to analyze the behavior of a pot heating on an electric stove. The heating element is modeled as shown in Figure P4.54. Find the "heat capacity" of the burner, $C_S$, if the burner reaches 90 percent of the desired temperature in 10 s . Assume $R_S=1.5 \Omega$. (FIGURE CAN'T COPY) Figure P4.54
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The heating element of an electric stove consists of a heater wire embedded within an electrically insulating material, which in turn is inside a metal casing. The heater wire has a resistance of 20$\Omega$ at room temperature $\left(23.0^{\circ} \mathrm{C}\right)$ and a temperature coefficient of resistivity $\alpha=2.8 \times 10^{-3}\left(\mathrm{C}^{\circ}\right)^{-1}$ . The heating element oper- ates from a 120 $\mathrm{V}$ line. (a) When the heating element is first turned on, what current does it draw and what electrical power does it dis- sipate? (b) When the heating element has reached an operating temperature of $280^{\circ} \mathrm{C}\left(536^{\circ} \mathrm{F}\right),$ what current does it draw and what electrical power does it dissipate?

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Transcript

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00:01 First question we're looking at the heater wire within an electric stove.
00:07 Now the question for the first part, we are just finding what is the current that is being drawn at the start, as well as the power, which it dissipates.
00:19 So to find its current, we can use i equals to v over r.
00:25 We are given that the voltage is 120 volts, and the resistance at root temperature is just 20 oms, right? so it's just when it turns on, right? so the resistance is still the same as at room temperature.
00:40 So the current from here should get 6 ampias.
00:45 The power dissipated, we can use p equals to iv.
00:50 So 6 times 120 should get 720 watts.
00:59 Now we are given that the stove is allowed to heat, heat up.
01:07 Until it reaches a temperature of 280 degrees.
01:15 And we want to find what is the current now as well as the power...
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