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Problem 56

You have a 12 -V battery, some wire, a switch, and a separate coil of wire. (a) Design a circuit that will produce an emf around the coil even though it is not connected to the battery. (b) Show, using appropriate equations, why your system will work. (c) Describe one application for your circuit.

Answer

a) When a conductor is rotated in a magnetic field, or when the flux linked with the conductor is changed, an emf is induced in the conductor according to Faraday's law of electromagnetic induction.

b) $M\left|\frac{\Delta I_{1}}{\Delta t}\right|$

c) The coupling between the primary and secondary coils in the transformer is based on mutual inductance.

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## Discussion

## Video Transcript

in this question, we are given a 12 volt battery, some wires, a switch on a separate coil of wire. And we are, too, according to our A design, a circuit that will produce an E M f around the coil even though it is not connected to the battery. So I'm going to design something that also involves an iron core, and I will explain the purpose of having this firing core in a bit. So I'm gonna name this the iron core. Alright, So first, I am going to wrap. Um, the wire said I'm given around one end of the iron core. And of course, I need Teoh connected to a battery source. And I will also install the switch right here. So this is the switch. Is this the battery? And is this the wire that you're given now? You also have another coil, a separate coil of wire that is not given or it's not connected to the battery right here. So this is that's separate oil. So how is it that we can induce an E. M f in this coil even though it is not directly connected to the batter B? Well, the moment. You close the switch right here. What will happen is you will have now a running, um, current within this primary oil right here. So note, because you just close to switch the current is not yet steady. It is still increasing, even though it takes a very short time to get to a study value. But in that split second, it is still increasing. So when you are, your current is increasing through the first coil, and this essentially acts like a Solon oId. It will then induce a magnetic field that is also increasing. Okay, so the point of having an iron core it here is so that it can confine the magnetic field produced by this current within the Army Corps so that it's not spread out. And so whatever a magnetic field is produced by the running current right here will now pass through the second coil, um, without escaping outside of this iron core. So because the magnetic field is changing through the primary coil, it is also changing through the secondary coil, thereby inducing um, an e m f in the secondary coil, and therefore in inducing a current in the secondary coil as well. So all of that is to say, um, this is a classic example of Faraday's induction. So what better equation to use to describe the situation than Faraday's law of induction? So, um, F is equal to end times the changing magnetic flux divided by the changing time. So n stands for the number of coils you have number of turns you having that coil. And in this particular case, the changing flux comes from the change in magnetic field through the secondary coil area of the coil. Doesn't change over a period of time. So this is how I would, um, explained the scenario using equations Finally, and the question asks you to describe an application for your circuit. So in this particular circuit, what you see here is actually a transformer. So transformer, um uses, uh, two coils, primary and secondary. It is the coupling of these two coils that allows a step up or a step down of the source voltage to an output voltage. In other words, if your source voltage is a lot higher than the device that you use needs, then you're just gonna use a step down transformer to transform quote unquote the source voltage to an appropriate amount of output voltage that you need

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