A cardboard tube is wrapped with two windings of insulated wire wound in opposite directions, as shown in Fig. E29.20. Terminals a and bof winding A may be connected to a battery through a revers-ing switch. State whether the induced current in the resistor Ris from left to right or from right to left in the following circumstances: (a) the current in winding Ais from a to b and is increasing; (b) the current in winding A is from b to a and is decreasing; (c) the current in winding A is from b to a and is increasing.

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Accepted Answer

Hello, fellow physicists today, we're gonna solve the following practice prom together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem, consider two windings in a transformer wrapped around. As shown in the figure, if the terminals P and Q are connected through a mechanism to a battery such that current can flow in both directions, then determine the direction of the current induced in resistor R for the given conditions I increasing flow current in winding P from P to Q I I, decreasing flow current in winding P from Q to P and II I, increasing flow of current from Q to P in winding P. Awesome. So it looks like our final answers are our end goal. Ultimately, we're trying to solve for three separate answers we're trying to solve for part II I and II I Awesome. So looking at our figure that's provided to us, we see that winding hue is represented by this dark, thick bolded black line that's crawling around like this broad shape. And it's connected to a resistor which the resistor is rene represented by this jagged black bold line which a jagged line usually denotes a resistor in a circuit diagram. And we have our capital R above it representing the resistor. And then we see winding P is a thinner black line wrapped around this like cylindrical rod shaped thing. And we see on the far right of our figure Q and then on the far left of our figure, we see P so point P and point Q, I guess if we could call them point B point P and point Q. So we're trying to figure out the direction that can flow in both directions. So we're asked to determine the direction of the current induced and resistor R for the given consi given conditions. OK. So now that we have an idea of what are, what's going on in our figure, let's read off our multiple choice answers to see what our final answer set might be. So, A for part I is left to right for I, I, it's right to left. And for II, I, it's right to left. For B for I, it's right to left. For I, I, it's right to left. And II, I is left to right. C for I is left to right, I, I is right to left and II, I is left to right. And then finally, for D for I, it's left to right and I, I is left to right and II, I is right to left OK. So first off, we need to recall and apply lenses lock. Remember that the field of the induced current will be directed to oppose the change in the flux within the secondary circuit. Also remember that the direction of the induced current will depend on the direction of the external magnetic field and whether the flux is due to this field is increasing or decreasing. So now we can solve for part I once we consider all of that. So now we need to note that the magnetic field in terminal P is increasing to the right, the flux is also increasing. Therefore, the flux will also increase. Thus, the field due to the induced current in terminal Q is to the left. So the induced current will flow through resistor R from the right to the left. So right to left is our final answer for part I. So once again, the induced current will flow through resistor R from the right to left direction to produce a magnetic field to the left direction. So now we can solve for part I I. So we need to note that the magnetic field in terminal P is to the left and is decreasing, the flux will also decrease. Thus, the field due to the induced current in terminal Q will be to the left. Therefore, to produce a magnetic field to the left, the induced current must flow through the resistor R from the right to the left direction So right to left awesome moving right along. So now we could start solving for part II I. So we need to note that the magnetic field in terminal P is increasing to the left, the flux will also increase. Thus, the field due to the induced current in terminal Q is to the right, in order to produce a magnetic field to the right of the induced current, it must flow through the resistor R from the left to the right direction. OK. So we did it we solve for this problem. So it's very vital for a problem like this. It's super important to have a strong understanding of the conceptual physics involved with circuits and solenoids. And once you have a strong conceptual understanding of the physics that's going on here, a problem like this will be very easy to solve. So if this is seems difficult to you, I would suggest just, you know, reading up on, you know, on solenoids and circuits and get the conceptual physics on lock and then a problem like this will be a breeze. So looking at our multiple choice answers, the correct answer has to be the letter B I which is right to left, I, I is also right to left and II I is left to right and that's it. Thank you so much for watching. Hopefully, that helped and I can't wait to see you in the next video. Bye.

Verified Solution

Key Concepts

Electromagnetic Induction

Lenz's Law

Right-Hand Rule