Problem

(a) What is the hot resistance of a $25-\mathrm{W…

Problem 71 Hard Difficulty

Construct Your Own Problem
Consider an electric immersion heater used to heat a cup of water to make tea. Construct a problem in which you calculate the needed resistance of the heater so that it increases the temperature of the water and cup in a reasonable amount of time. Also calculate the cost of the electrical energy used in your process. Among the things to be considered are the voltage used, the masses and heat
capacities involved, heat losses, and the time over which the heating takes place. Your instructor may wish for you to consider a thermal safety switch (perhaps bimetallic) that will halt the process before damaging temperatures are reached in the immersion unit.

Answer

(a) $\mathrm{SR}=22.9$ $\mathrm{omega} $
(b) Cost $\mathrm{S}=0.209 \mathrm{S}$ cents

Related Courses

Physics 102 Electricity and Magnetism

College Physics for AP® Courses

Chapter 20

Electric Current, Resistance, and Ohm's Law

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Video Transcript

In this particular problem, the energy dissipated. Ban electrical plans in terms of power rating is giving us first. We'll start with the energy dissipated, which is giving us capitally. It is a multiplication of power and time. So I just write it down. He stands for energy B stands for power and he here indicates the time short in which the device WAAS operator now as energy question is Regan as easy quit too. We square upon our and multiplied by now. We can write this because he's equal to that. Its power is equal to we square upon O r No, In this case, as we already know that easy quit awarded JJ and R stands for resistance. Now let's start with be part Suppose a cup contains, uh, three minutes Reporters. I just write it down like considering a cook has 300 milliliters of water and at room temperature off Trinity the senses. The heater takes seven minutes to heat water and we can consider the temperature changes we can consider the temperature change from 20 researches. 200 degrees is off its boiling point Now the amount of energy I'm right here. So the amount off heat. Energy, which is cute, is given us em into sea into tell dirty and we're defined. His bottom occurs first. So Am music, too myself. Walker, which we have Cygnus to yonder Emma, which is to be 300 cramps at the same time. See sense for specific eat, which is 4.18 Jules for Graham, Gigi Senses on Guitar D indicates a change in temperature, so write it as temperature change. So in order to find the change, it will be 100 minus 20 degree senses. So we're just coming as 80 degree senses. So let's find the paramedic you, which is amount of heat energy, which has given us em into seeing Judy. So we'll write down the values 300 grams multiplied by 4.18 grams. I'm sorry, Jules. Poor Graham degree senses and multiplied by you Delivery senses. We get the answer as 10 born 03 into generous to four. Jules, and this is the amount of heat energy required is on. Sure. Next step. See, since you already know that energy is given in dumps off a question that is Reese, where bone are much too kind of I t. Therefore, in order to calculate resistance, it will be re square upon e much apart by t. Now let us substitute the values as he's equal to, say, seven minutes, which are converted into seconds. First, BZ quit to one trained words the amount of energy which we have already got 10.3 into tenderness to four jewels. He wanted to cover the resistance. Now I'll put 1 20 square because it's three square might ignited by D, which is seven into 60 seconds and internally divided by the amount of energy that is 10 born, 03 into tennis to four jewels, that is Katherine This and we get the answer as 60.29 homes. Therefore, we can take the resistance as broke, similarly six year olds so we can write it as immersion heater, immersion, heater's resistance. While new he's off 60 homes. This will be around. Sure, let's think about the Bardina. Suppose then sends particular work is the cost of electricity, so I'll write down. Suppose we're taking 10 cents Particular work you don't watch over is the cost off electricity. So then we need to convert energy into killer what are first. So therefore I write it down. Energy in this case is required to against every shock 10.203 into tennis to pour jewels divided by T 46. Enter canister six shoes, which is coming gas 0.278 You know what are I? Write down the reason here a seance. One kilo watch. Our is equal to 3.6 into Dennis to six years. But this is what you need to remember. With us. The cost will be 10 cents working or what over multiplied by the amount of energy which is 0.0 through 78 kilowatt hour. I can't reading this. We get it as 0.278 Sense that really to spend so right Finance of years Such a real cost will be 0.278 cents. Could be

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