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Problem 42 Hard Difficulty

A coffee maker is rated at 1 200 W, a toaster at 1 100 W, and a waffle maker at 1 400 W. The three appliances are connected in parallel to a common 120-V household circuit. (a) What is the current in each appliance when operating independently? (b) What total current is delivered to the appliances when all are operating simultaneously? (c) Is a 15-A circuit breaker sufficient in this situation? Explain.

Answer

a. 10 \mathrm{A}, 9.2 \mathrm{A}, 14 \mathrm{A}

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Video Transcript

now in this particular problem the coffee maker toaster and waffle maker. These three give Mons air connected in Madeline with the supply off 1 20 Would no Asper step A. We need to find current in each of plans. So we need to make use off expression of power. So all right, down to find I got it. In each appliance, we can use expression off power in order to find the current through each branch. So therefore PCM is equal to total world ish Might applied by Got it threw. Coffee maker your P C M stands for power across the coffee maker which has given us trail under wards Will make use of that 1200 wards is equal to the up notable day. JJ is 1 20 world with Children. Men seem across all the plans is since it is gonna get in battle multiplied by Karen threw coffee maker. So therefore, in order to find currently, coffeemaker will take the ratio off 1200 21 Ready. So therefore, got into a coffee maker, they'll be off damn abuse. This is our first answer. No. In the next step will calculate current through the toaster so again. Well, write it down. Power grows. A toaster is speedy is equal to product off, cutting through the toaster and work it across the closer that is ready. Therefore, well, what it grows with Your story is given as 1100 watts current that we need to find out and a mortgage again remains the same, which is 1 20 words. So therefore, I D is equal to 1100 wards divided by 1 20 words. So we're just coming Gas 9.167 amperes So current a grocer is 9.16 seven years. Now let's find out the turtle that is garden through the waffle maker. So we used the same expression but denoted as be WN, that is power across the waffle maker is equal to total wordage. Want you played by current which is flowing to waffle maker data for it has given us 40 100 words. We write it down for 300 is equal to 1 20 multiplied by current so therefore got into wolfram maker is equal to 40 100 divided by one brandy. So finally we get the current through a waffle maker as 11 born, 67 appears Billy just put it in the bracket. This is the answer for the 3rd 1 No, let's move to step be. We need to find the tour group currently work to the all appliances, so write it down lit Total current Did the word to all appliances be I, which has already been shown in the diagram. So therefore we can make use off K seal and we can ride this expression that is coffee. Make a garland so sick I didn't and Wolf will make current so current which is enduring and leaving the door. So this is the expression by K jobs current room that we have Georgia Dome. So therefore now we have over the three values that is stamp here bless 9.167 beers unless 11.67 amperes. So we get to finding value by adding this together that is 30 point a 37 amperes. Therefore, AII is equal to 30 point a 27 appeared. This is the answer that we have caught which is a total current delivered to all appliances by the main battery. No, In the next step, we're right down the answer whether we plan to use 59 beer circuit breaker to write the statement for that. And that would be four steps see off If Guinevere Circuit breaker in this case is not suffer. Shoot and let me write the reason for that in this situation because due to recurrent, I think which is off Isaac would do 30.37 ampere exceeds the limit off the circuit blinker. So your total current is actually exceeding the limit of the circuit breaker. So all appliances could not be operated simultaneously if we'd planned to use 59 beer circuit breaker. So basically, we cannot use this 15 and your second breaker because it is exceeding the limit off the total current. This will be our final answer.

Top Physics 102 Electricity and Magnetism Educators
Christina K.

Rutgers, The State University of New Jersey

Zachary M.

Hope College

Jared E.

University of Winnipeg

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McMaster University

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