the-current-i-in-a-in-a-certain-electric-circuit-is-a-function-of-the-time-t-in-s-and-a-variable-res

Name: the current i in a in a certain electric circuit is a function of the time t in s and a variable res
Uploaded: 2019-07-24
Duration: 3 min 36 s
Channel: Numerade
Description: The current $i$ (in $A$ ) in a certain electric circuit is a function of the time $t$ (in s) and a variable resistor $R$ (in $\Omega$ ), given by $i=\frac{6.0 \sin 0.01 t}{R+0.12} .$ Find $i$ for $t=0.75 \mathrm{s}$ and $R=1.50 \Omega$.

Question

The current $i$ (in $A$ ) in a certain electric circuit is a function of the time $t$ (in s) and a variable resistor $R$ (in $\Omega$ ), given by $i=\frac{6.0 \sin 0.01 t}{R+0.12} .$ Find $i$ for $t=0.75 \mathrm{s}$ and $R=1.50 \Omega$.

Margaret Keymakh · Accepted Answer

so in this question, were given that P is equal to our I squared under arrest ified dp dt or the derivative of this right here. We were also given some other conditions. So we&#x27;re looking for that AT T is equal to 1/3. We&#x27;re also told that I is equal to sign of four pi ti. So first, let&#x27;s rewrite this equation right here plugging in, um, our expression for I So this is gonna be equivalent to P is equal to are, which is a constant times sign square since we have ice crowd right here, So sine squared of four high t Um and now we&#x27;re ready to actually take the derivative. So D p d t, um, is gonna be equal to first. Our outer function is sign of four pi t squared. So let&#x27;s use the chain rule. Let&#x27;s multiply by two. And this attract one from the exponents. So that&#x27;s gonna leave us with two r Sign of four pi team. Um, so next we have signed. So we&#x27;re gonna take the druid of that, and that&#x27;s gonna give us co sign co sign of four pi ti. Um and finally, our most inter function is for pi ti through. That is just gonna be four pi times for pie. So this is equal to yeah, hi are and again or is just a constant times sign of four pi ti times co sign of fork i t. So now we&#x27;re actually ready to plug in what we&#x27;re given in this question. So we know that we just write this on the side. That t is equal to 1/3 and our is equal to 1000. So it&#x27;s part of that into our equation here. So we&#x27;re gonna get that DP duty AT T is equal to 1/3 is equal to eat Pie times 1000 Um, a times sign of four pi over three times co sign of four pi over three. Um, if you multiply this, you get about 10,000 882 0.8 watts. So this right here is our final answer.

Alex Breitweiser · Answer

Hi all. Let&#x27;s be here with another question on electric current and resistance from Chapter 25 of Jean colleagues, physics for scientists and engineers. So this problem tells us we have an equation for an electric current. We&#x27;re just given by eye is equal to 1.80 amps. Times the sign of 210 times T Ortiz in seconds set of may sound a little bit weird, but bear with me because any time that we see an equation like this, we think back to our periodic equations, where usually want to describe a periodic function, we do it in terms of its maximum amplitude, which here I&#x27;m gonna do No, I zero time sign of omega. Some sort of angular frequency times Time t So you&#x27;ll receive it. We have I zero. Our maximum amplitude is 1.80 amps. And omega, which is our angular frequency is 210 and the units here gonna may sound a little bit weird. It&#x27;s going to be radiance percent per second, of course, makes sense because time teas in seconds Radiance actually is not a unit, but we put it there to remind us the fact that we&#x27;re using omega as an angular frequency rather than a cyclic frequency. How long it takes to come back to where we started. But the first part of the question actually asked us for just that. What is the frequency of this? What is the frequency of this current? So to get that we calculate their frequency f amount of time it takes us to get back to where we started is equal to omega. Are angular frequency divided by two pie because there are forced to pie radiance in one cycle if you plug in the numbers here we used 210 radiance per second for Omega, divided by two pi. We should find they have a frequency of 33 0.4 per second or weaken. Right, That is 33.4 hurts. The second part of this question asked us what is a root means? Square current? If this is our equation for current, Well, when we&#x27;re looking for a root meets square of a periodic signal, we know that our r s current is just gonna be our maximum current I zero divided by the square root of two and putting the numbers that they gave us. Where eyes Here is 1.80 Epps. We&#x27;re going to say that a root means square current is about one point to seven m&#x27;s where again We&#x27;re using three significant figures here because they give us three significant figures in the problem. Finally, for part C, we know that our voltage is equal to ay times are and they&#x27;re asking us to write down the equation for the voltage as a function of time. Well, the resistance is given to us is 24 points 0.0 homes and we know that it&#x27;s probably not gonna be changing. So we know that eyes 1.80 amps times the sign off to 10 times t We know that our resistance is 24.0, homes. So we&#x27;re flying all these together we can most like 24.0 by 1.80 to find 43 0.2 volts as their maximum voltage. And now we have our periodic function, which is just gonna stay the same to 10 times t where t is again insides. And this is now going to be our equation for voltage as a function of time

Farhanul Hasan · Answer

Okay, so the current takes us. I&#x27;m sorry. Delacey Current form. Ah, where I equals eye. Not the max current or p Current times sine omega t t is tea. In this case of Omega is, um, whatever the coefficient of tea is. And so here we have I equals ah, 1.4. That&#x27;s the max current. Ah, sign to 10 t 7 to 10 is Omega. So Omega&#x27;s 210 radiance per second is the sport, eh? Um And so therefore frequency will be omega over tea pie. So to 10. Rapper second over to pie give to pyre. Aidan&#x27;s giving you frequency of Hertz off 33 hurts in part B. We&#x27;re using the fact that our mess current is one over squared of two times the max current says there&#x27;s one point floor lamps over square of two, giving you 0.990 imps. And finally, voltage, we know from Mom&#x27;s Law is equal to I r. And so I is 1.40 amps. Times sign to 10 t um, times are which is ours. 24 arms and so am time zones is bolt. So you multiply 1.4 with 24 you got 33.6, uh, volts times signed to 10 to. In other words, voltage is equal to 33.6. Sign to tend to you units of votes, and that&#x27;s it.

Khoobchandra Agrawal · Answer

Yeah, have everyone in this question it is given with the wire operated straits forgettable Got a is flowing according to the question one quite it. So I know one did pen in Tohti on its current major in MPs. In the first part, we have to calculate frequency or peppering on in second, but we have to write right the equation off work. It&#x27;s what can you tell the place we are solving the first part. What entries given one point it sign up 220 in Generally question off. Current is I gotta go. I know. Sign up by having duty. When we compare the equation, but in tow by frequency, Dukie will be 200 million cookie so frequencies to be meter one drink and divided by two bite. That is who would get that two into three points? But for by having that I do 3.14 So propensity 33.4 hurts. This is the antidote pushed park. Not in taking part. We have two very question. What a difference across the quite will be correct into registrants car engines given one point it sign up, one dripping in to be on the distance of the white is given for giggle. So on solving we will get they will be 0.56 Sign up. One did that in two. D and unsuitable meatball. So this is the answer of this question. I hope everybody has understood. Thank you for

Donald Albin · Answer

we are given V as a function of T equals 160 volts times the sign of 120 pie. See, um, were also given that are is 50 owns Well, V equals I Oh, are. Or rather I want to use lower case like were used in the book V as a function of T is I as a function of t times are so all I have to do is divide by our so I as a function of t is just V over R, um 160 divided by 50 is 16 5th the no, not V amps. Sign 1 20 pie T. There is no phase shift. Uh, because this is a resistor, so that is the answer.

Problem

The reciprocal of the image distance $q$ from a l…

Problem 37 Easy Difficulty

The current $i$ (in $A$ ) in a certain electric circuit is a function of the time $t$ (in s) and a variable resistor $R$ (in $\Omega$ ), given by $i=\frac{6.0 \sin 0.01 t}{R+0.12} .$ Find $i$ for $t=0.75 \mathrm{s}$ and $R=1.50 \Omega$.

Answer

$0.028 \mathrm{A}$

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Allyn J. Washington, Richard S. Evans

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$0.028 \mathrm{A}$

Basic Technical Mathematics with Calculus

Lily A.

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Michael J.

Vectors Intro

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Lily A.

Kayleah T.

Kristen K.

Michael J.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus