questions-1517-all-refer-to-the-below-circuit-diagram-if-switch-s_2-is-connected-to-point-a-but-swit

Question

Questions 15–17 all refer to the below circuit diagram.
If switch $S_{2}$ is connected to point A but switch $S_{1}$ is left unconnected,
what is the current through the resistor labeled $R ?$
(A) $\frac{9 V_{2}}{R}$
(B) $\frac{13 V_{2}}{3 R}$
(C) $\frac{3 V_{2}}{13 R}$
(D) $\frac{V_{2}}{9 R}$

Nishant Kumar · Accepted Answer

in this problem switch as two is connected to Point A&S. one is left unconnected. This results in the right most arm of the circuit with two resistors in parallel being out of the circuit, and we are left with the left most resistant to our and the two resistors in parallel to our in for our in the middle branch of circuit And the Voltage v. two. And we have to find out the current through the sister are. So first we&#x27;ll find the equivalent resistance so we can see that they couldn&#x27;t resistance will be the cities of to our our and Parallel combination of two. R. and for our so the covenant resistance is Are equivalent equal to two are plus our plus parallel combination of two R. And four hour. Which can be given by two or in 24 hour. Bye to R. Plus four. So This is three are plus four. Are by sorry four are by three. This gives us 13 are by today. So current given by battery would be equal to voltage battery by equivalent resistance equal to B to buy 13 are by three called to three. We to buy 13. Now we can see that the battery here is in serious with the sisters are so the current through the sister are will be equal to I I will be called to current given by the battery. So the current Through resistor. R is simply three v. 2 by 13. Are this complete solution? Thank you.

Ze-Han Lee · Answer

All right. So in this circuit, if way Ah, thanks. Disconnect as one. And ah, we connect us to to a So we see that that equipment circuit ihsaa this part. Ah, so this will be the equivalent circuit, right? So Ah, then we see those. This too are in this four. They&#x27;re they&#x27;re connected. Parable. So the combined resistance off them is one over. Sorry, it&#x27;s the two aren&#x27;t times four bye bye to our plus four, which gives you three. 41 of three kinds are so total resistance in the circuit is 43 times are plus R plus two are ray. So this gives you the ting over three times are so the current inside this Ah ah circuit is, uh, my equal. Free to do. Bye bye. 13 over three times are right. So this gives you three V two over 13 are okay.

Ze-Han Lee · Answer

All right. So in this problem Ah, so as to is ah, left unconnected and asked why is connected to be so we simply we have this circuit free. So, uh, yeah, this is a connected So the equivalent resistance in the circuit ihsaa are So are these over here? Okay. And two are four there in parallel. So the total resistance is to our times for Do you like to our plus four and, uh, the this to their Olsen parallel. So that&#x27;ll resistance. All this, too, is, uh, well, over three are times went over to our they lied by. Went over three are plus one over to our Okay, so this gives you 38 over 15 are Okay, so the current inside this is the circuit equal V one over r acute equivalent. So there&#x27;s our equivalent so equal 15 we want over 38. Are you okay?

Ze-Han Lee · Answer

All right. So in this problem, as one as to their both unconnected. So in that way we see that Ah, there is actually no current through this. Ah, through some of the resist that label my arm. Okay. Occurrence in 20

Abhishek Jana · Answer

so and this circuit we see that all three and our four are in parallel connection in the circuit. And our one is in Siri&#x27;s with these two. Now what happens is for from ours one we have the total current I totaled. That goes too. And then it gets divided into these toe resistors because they&#x27;re in serious can apparel connection. And when the switch is closed, then we have another resistor which is in Parral connection with archery in are for So what happens is when a resistor is in parallel connection. The equivalent resistance is Lord so so far Parallel connection. The Cuban resistance is lower than, um the individual. Ah, our And for serious connection, it&#x27;s the opposite. So here the equivalent resistance is actually greater than the individual art individual art. So since we&#x27;re adding another resistor here Sorry, Camilla, injuries in resistance is decreasing. Now if the equivalent, for instance is depleting. So that means the this part taken for instance, in this party is now Lord and what that means is will have ah, an increase in current because our art is decreased now and ah, sins the are one is in serious with all this, we there will be an increase in voltage here because again like we need to start with the here. And we need to end up and Ciro years so that the whole job is consistent So the voters will increase around this region. And then if we consider all the parts individually so around this part of all this drop will decrease. So that means. And since it&#x27;s a parable connections So at each note Ah, the voltage drop, it seems. But initially, since they there were only two resistors, the value got decreased. Once we added the other one, that means a voltage drop will decrease once we add the third one. So that means all together from initial hold, age ofthe art, an art for it will decrease. And since our two didn&#x27;t have any old age once we connected it it some hold, it appeared here. So that means the voltage will increase around this region. And since this guy&#x27;s in serious, so four days will increase here as well. So if we write that down with me ca near, uh, this part. So miss, give me one second, okay? Ah, yeah. So in part a voltage across this will increasingly college everyone so everyone will increase. And then we call the voltage across here veto. So we won and Vito when Increase and Vetri and people will decrease four decrease. And similarly, since the same by similar argument we can see that the current from in this case, the current will become something from zero. Because when the switch was not kind but they were no current passing through it. So the kindly increasing and for this case, since the voltage increased. But our Ari&#x27;s constant here, that means the current will increase as well. And by similar argument, these two cases since the voltage drop decreased. So our current will decrease as well. So I won and I do. So these are the current&#x27;s off this one, and this one respected me when increase and I t. And I for will decrease and for part, see when, ah, we want to know the power output. So what happens is since there&#x27;s an increasing current I won and I won is equal to the total current because this guy&#x27;s in serious connection with the battery. So let&#x27;s call it Ivan as well, eh So that means the total current drawn by this battery has increased. And since the voltage output is the same or the battery, that is Ah, the battery that&#x27;s connected is not changing. So that means. And since our current has increased, our our power will increase because we know that power is full This times the current. So our power output will increase. So we know power is V times I and that will increase. Okay, Now for the second part Ah, we We are given some values and we see that they all have the same resistance and the barrier is twenty two volts. So we need to find the individual currents and across each resistor. So what we do here is we see that Arjun are four are in parallel and the switches open. So that means we don&#x27;t have to worry about auto. But then our one is in Siri&#x27;s without you in our for so what we do here is first we need to find equipment resistance and that is given by this formula. Where are one is in Siri&#x27;s with these two guys? That&#x27;s why you&#x27;re adding are one to the Cuban resistance off Artie and are for if we do that, we get some value like this. So that&#x27;s thank you for the resistance. And if we draw ah, diagram, it gives us something like this where this is our V and this is the Cuban resistance. So if that&#x27;s so, that means our total current will be the barren Hold it over our cue. So that&#x27;s the V. Very Andi, I total is going to be twenty two, which is the voltage of the barony divided by the secretive instance on That gives us this twenty point zero nine four six two m&#x27;s. And now why This is equal to ay one. Because this resistor isn&#x27;t serious connection with the Barry. So that means that all can, as we mentioned, the total current flowing to our one is same as I want. So that&#x27;s why this is our I won. No, go get the voltage drop. We have to use the eye, which is equaled. Ai ai ai One times are one. This is using arms law and that will give us The voters drove across our one. So that means if we know our one, we know the voltage rather cars across this far. Andi remembered this, which is open, so that means there&#x27;s no current passing through it. So we&#x27;ll drive across this part on the artery are for and that&#x27;s going to be the total of all days, minus this fee one. And that gives us seven point three t four holes. And so, if you want to calculate the current since they&#x27;re in peril connections, so for three and for the voltage job will be the same. So that&#x27;s why we took this. And since our two and all three are same as well. So whatever current we get as I tree, that&#x27;s going to be called try for. So the final answer that we get here is we divide our for VP by one fifty five forms and that gives us an answer is point zero four seven three two grams. Okay, so this is our I three eye for and this is our I want. Right now we have to do the same calculation. But now we have another another. Resistor are too is in Siri&#x27;s. So what we do here is we do the same calculation, but here will had add an extra term which is one over R to because that&#x27;s in serious connection. So it&#x27;s going to be our one plus the simple Akhil of our two, plus our three, plus our four. And since we know that these values are all equal, we can plug in and they&#x27;re one fifty five home. So we can plug in the number and get our, ah, equivalent resistance as this. So as we can see that the resistance that we got here is higher than this, So that proves that if something is connected in Siri&#x27;s, that lowers little resistance. Um, so similar way we find the total current. What is the mattering divided by the Cuban resistance and that will give us twenty two balls divided by to our sex find seven homes, which is going to be goingto zero point one zero six four AM&#x27;s on That is equal to I want right. So once we know I won. Ah, Once we know I won, We need to find the voltage drop. And then from there we get the voltage of across the parallel resistors. So let&#x27;s get on, Dan. So the one equals I wan times are one and I want is this guy and our one is one hundred fifty five. So it&#x27;s going to be one zero, six four hands things. One, five, five homes That will give us a sixteen point forty nine holmes. So the voltage drop creepy will be V very minus the one on DH, which is five point five one worlds. So ifwe, if we know VP now, we can find out I three eye for and in our case we confined I too as well, because again the voters job is seen. They&#x27;re and okay, so it&#x27;s going to be I three or four because we don&#x27;t have our to connect it. It&#x27;s going to see are for, um So now hi, tree when b vaping divided by artery ah, which is equal to ay to physical I for And if we put the number we see it&#x27;s five point five one rolls So five point five one fors divided by artery that is again one fifty five bombs. And that will give us a current as it was, you know, applying zero three, five, five. And so that means the prediction that remain in Barbie are all confirmed. So that&#x27;s the three currents I ti I I do and I for and that&#x27;s our I won. Thank you

Ren Jie Tuieng · Answer

What got show? Were given two different circuits. Uh, we trifle able as a and B. So a starts to get a top and peace to you people. Why did he seem some of the, uh, Petrie&#x27;s? It&#x27;s really similar resistance in the same positions. But only difference is 30 direction off. A battery for V two is different, right? Is shot over, like between A and B. We&#x27;re going to see how this affects our current. So first off, uh, gonna assume the Democratic current. All right, that is for a you&#x27;re gonna saw for the first. I&#x27;m gonna assume this is current I one since he passes true resistor want and in this junction. But I assume dirty current flows in this direction. This real call I to and over here, we&#x27;ll assume that it is doing in this particle traction. We&#x27;ll call this tree. So from this junction over here, this junction we use coach off through we should be able to get a get an equation. I will be I one plus I tree goes to to knicks. I&#x27;m gonna use cut. Ah, you cut your shoe to look at different loops in our circuit and we gonna use these two groups? So first up is and he could twice Sorry. This is ah twice don&#x27;t waste direction on the left in sight. Right for the small group and then being included already Lunch crosswise direction But for the altar. So these two loops. So for the first look we have passing through the battery everyone Dennett puzzles true one in the same direction as current. So we gets one I want so u minus a We know what I want. Yeah, he pauses to our 2 50 seem direction again. So this are too. It is 20 by coach Also the only question is gonna get poopy out rich. First we postulated battery in the right direction so that we head up to you. Potential difference. So that&#x27;s few one. They passed a veto but in the wrong direction, right from plus to minus. So we must subject away too. They re postural our tree If I treat in the same direction is the current that we assign So don&#x27;t be are tree I treat then next repulsed you are too Today&#x27;s are too high to create at 20 So over here we have triana loads eye to eye tree and I won. We treat questions. You should be able to sof this simultaneous equations. So one off the way is to, uh, reassign I to my eye to really know it&#x27;s he goes toe I want plus I tree So we substitute that to an equation Say, ah, discretion over here will be the second equation We will get to undaunted the secretion which is I one and I tree we make I want the subject for no So we get I when it goes toe I tree times something we substitute debt. Uh, sorry. We make I to we make treaty subject allergy formula since I took equation has I tree over here and every substitute Archie into this equation as well as I to say secretion, we should be with self for the entire equation. So for our tree unknowns, you should get one two people. So my six gm&#x27;s I, too to be sure point for many years and interesting. You get i tree to be, uh, close, too negative. 2.2 years in the reason why is negative because we assigned t direction off the current wrongly so the actual current will be in dis direction. All right, this is the tree correct direction. So the negative sign just tells us that it should be in this particular direction rather than the direction that we assigned it to be next. You&#x27;re gonna do the same process for Oh, it&#x27;s against the kids. I assume the Sistine direction of the current I one I to I treat. We have very, very similar equations. Ah, but this time it&#x27;s gonna be slightly different for ah, equation the big look. So we&#x27;re gonna do the same thing, this small upon the left and any big group or the outer The first equation would be the junction room. So that&#x27;s you seem I want us. I tree close to I to the second equation ISS the small look over here on the left, in sight in the cut wise direction. First we passed the battery view one in the right direction. Let me puss, I want one. Not very parts I two r two create their 20 for the outer past few. One for us. Very pass veto Seem correct. Order from minus to plus. So we get up to go. Very pass Tree artery. Very plus I too want to create that zero. And in this case gets I want because 2.4 mediums I to it goes toe point fight too medium and I treat would be close to one point for eight years. So old tree i d right direction that we have actually assigned like so they are in this particular order to calculate what is the power output? Like what? Tasty. Participated by a short circuit. We make you softy current February phone It&#x27;s a poet goes I square are right We know the current passing through each off the resistor Israel Asti Resistance off the resistance So we just take I want square one last two square or two pass I treat square treat in the first case before the first Our first look we should get your point to me. What&#x27;s this for? A For B should get 4.5. Media wants just substituting in the current it e resistance. Finally et polo that&#x27;s being supply so we don&#x27;t add power supply. It must be close to the power being dissipated. So there&#x27;s Jesse course toe off these values. They really cooperated from the polity. Speed it

Problem

Questions 15–17 all refer to the below circuit di…

Problem 16 Easy Difficulty

Questions 15–17 all refer to the below circuit diagram.
If switch $S_{2}$ is connected to point A but switch $S_{1}$ is left unconnected,
what is the current through the resistor labeled $R ?$
(A) $\frac{9 V_{2}}{R}$
(B) $\frac{13 V_{2}}{3 R}$
(C) $\frac{3 V_{2}}{13 R}$
(D) $\frac{V_{2}}{9 R}$

Answer

C

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