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A 60-W incandescent light bulb is plugged into 240-V AC_ a) Determine the hot resistance of the tungsten filament of the light bulb(b) Determine the rms current.(c)...

Question

A 60-W incandescent light bulb is plugged into 240-V AC_ a) Determine the hot resistance of the tungsten filament of the light bulb(b) Determine the rms current.(c) Determine the peak current_Determine the peak power consumption of the light bulb_

A 60-W incandescent light bulb is plugged into 240-V AC_ a) Determine the hot resistance of the tungsten filament of the light bulb (b) Determine the rms current. (c) Determine the peak current_ Determine the peak power consumption of the light bulb_



Answers

A certain lightbulb is rated at 60.0 W when operating at an rms voltage of 120. V. (a) What is the peak voltage applied across the bulb? (b) What is the resistance of the bulb? (c) Does a 100. - W bulb have greater or less resistance than a 60.0 - W bulb? Explain.

Let's do part a. Well. The maximum voltage is determined simply from the army's will. Teach with the usual relation which is maximum Will teach is equal to route two times we are a mess, right? And here we maximum musical too blue too Multiply be 120 with 100 twenties root mean square Baltes and therefore maximum voltage is equal to 170 walked Now let's to part B The resistance is determined from given armies Will Tate in power. So our is equal to we are timis root Mean square Uh, Walt It square divided by p Well, we are mrs 120 square, divided by 60 and therefore are is equal to 240 arms right? And now we do part c Well, a scene from the relation the resistance will decrease for a bulb with higher Well, we're so we hire with higher power resistance decreases resistance decreases decreases right

Okay here we have a question about power used in electric circuits. So we're told that the voltage used by a light bulb is 120 quotes is the standard all socket and the current that's used by the light bulb is 0.707 times sine of 314. Yeah, and time is time camps. So it's obviously an alternating current because it's dependent on the center. Um So the question I asked us, what is the frequency of the current? Okay, so the standard form for alternating current is i is equal to eight times sine of omega T. So obviously omega in this case is 314 and it would be 3.7 or seven. Um But to find frequency we just need to know omega because frequency is related to omega. Um uh Well the standard weight that these are defined as that omega is equal to two pi times frequency. So therefore frequency can determine is omega over two pi. So that's just what we're gonna do. We're gonna plug in 3 14 for omega. And we get that are frequency is 50 hertz. Yeah. Such are they answered. Mhm. And in part B they ask us for there are resistance of the film in the light bulb. All right. So we're gonna use owns off with this since we know the voltage and current. So we can just solve this for resistance. So we're going to divide both sides of the equation by I. So are is just the over I. V. We know to be 120 and I has a maximum of Israel 0.7 year old seven. So we just divide those and we determined that R. Is equal to 169.7. Oh, okay. Well Ramstein, should you do question to you? This question asks, what is the average power consumed by the light bulb? All right. So uh we know that P. Is equal to I square it R. Um And I has this sign term in it. Uh And when we square a sign term take the average of it, the uh we get one half. So the average power used is given by this formula of one house. Why not be not remember B equals Ir So this is really just um we can equivalently right. I not squared times are but this is the standard way that the equations timed. Um Either way we can we can do it since we know what ivy and our so we can just plug in I not which is your 0.77 and we can plug in V which is 120 fault. Uh And then of course we just need to divide by one half and we found that the average part and seemed is 42.42 lots. And we're done.

The question, we're talking about power circuits. Uh in this particular question, we have this container of water which holds 50 gallons and is being heated by the current running through. Her sister told that the voltage in africa is 120 volts and the resistance of the resistor three elms. The initial temperature of the water teen off is 11°C and the final temperature to you Is 53°C.. It was just being heated by um the energy that's dissipated across this resistor. The energy is of course power And we're told that the process is 100% efficient. That means 100% of the heat energy is going into eating the water. So power times uh, time.

Okay. In this question we have to I'll find out the grand I When the World Age V is equal to to 20 vote. In the second part of the question again, we have to find out there great. But this time the world ages 110 days, 10 more. In the third part of the question, we have to find out the power When the world stage is equal to 100 and 10 words. And from from the given data, The power is equal to 60 word. And the world age B is equal to to 24. So we know that the power and the family of the power is equal to way into I. So eyes equal to I is equal to be. How do we I went to SPS given a 60 what? And the voltage is given us to 24. Therefore, they couldn't I? We get a zero find 27 272 MPS. And in the second part of the question again, we have to find out the current. When the world rage is equal to 110 words. We know that the power can be written as being too I. But I can find out by dividing the power with the Old age as the power is given a 60 word And the voltage is given us 110 war. Therefore the current England 0.545. And beer. And in the third part of the question, we have to find out. And the power is the power is equal to we into I. So we have to find out the power when the world ages. 110 words. Therefore power become one handed in a 10 war multiplied by the current is U. N. S. 10 1, multiplied by fine. five 45 There. For the power Is equal to 61.


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