Problem

If we model the pore of a hypothetical ion channe…

02:52

Problem 92 Hard Difficulty

In the circuit shown in Fig. 19.73 $R$ is a variable resistor whose value can range from 0 to $\infty,$ and $a$ and $b$ are the terminals of a battery having an emf $\mathcal{E}=15.0 \mathrm{V}$ and an internal resistance of 4.00$\Omega .$ The ammeter and voltmeter are both idealized meters. As $R$ varies over its full range of values, what will be the largest and smallest readings of (a) the voltmeter and (b) the ammeter? (c) Sketch qualitative graphs of the readings of both meters as functions of $R,$ as $R$ ranges from 0 to $\infty.$

Answer

a. So the largest value of voltage in voltmeter is $V_{a b}=\varepsilon=[15.0 \mathrm{V}]$
smallest value of voltage is $\varepsilon-I r=(15.0 \mathrm{V})-(3.75 \mathrm{A})(4.00 \Omega)$ $=[0]$
b. From the part (a), as resistance $R \rightarrow 0,$ then the maximum value of current is
$\frac{(15.0 \mathrm{V})}{(4.00 \Omega)}=3.75 \mathrm{A}$
As resistance $R \rightarrow \infty,$ the minimum value of current is $I=[0]$
c. The below graph shows the variation of voltage with the resistance is
graph is not available

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Physics 102 Electricity and Magnetism

College Physics

Chapter 19

Current, Resistance, and Direct-Current Circuit

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Video Transcript

the circuit in question can be drawn like this. They have a 15 year old battery with four ohm internal assistance on We have an external here, stat that that will have a valuable assistance. Are the world intercourse over here on the imager? Is that in the second? But now you know that the current through amateur is simply they got into the second. Now the total resistance of the circuit is simply the sums off the tour assistant because they're in serious. That's our bliss. For so the current is simply old age by assistant, which is 1,505 are bliss, for that is the current so as our ghost from say hello to infinity, the current post from where our physical zero the current is 15 by four. It is 3.75 here on when to their assistance is infinity goes to zero by the world they just likely tricking. Now that is simple trick though the whole day across this battery is the same as the voltage across this resistance. If you notice that you can see that ward age is simply I r, which is you know I is 15 by for bliss times that distance is simply are another way to do it is we know that the effective image off a battery is it's in minus I r. We know that Emma is simply 15. My eye is 15 by four. Place are times the resistant is for home This again don't start Toby 15 point by four plus R r Now what is that in any approach will give you the same solution. But it's just that some approaches sometimes tend to be shorter than the other approaches. So in this case, but the resistance goes from zero to infinity. The whole days goes from its existence is zero This resistance become zero and with 15 are become zero. The numerator become zero on the word please reconsider. But again, when the resistance becomes infinitely though, notice that the numerator and the denominator put our port infinity. So what you can do is 15 are by four Bless our If we do it by our on both numerator and denominator, this becomes 15 by for by our plus one. Now, if you apply the limit, our tends to infinity 15 by one Best four by our for by are simply become zero and this becomes in ward. So old age goes to 1,500. So they can simply don't call quality to Niagara as their assistance goes from zero to infinity. The current, as you can see, goes from 3.750 But it goes as one by our so it looks something like this. This is 3.75 ward here. Similarly, for whole days it goes from 0 to 15. But remember that it goes something like this. It reaches its only a symptomatically because ofthe which is a violent from this nature. It is one by one by our form, that is it.

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