You have a 12 -V battery, some wire, a switch, and a...

Name: Problem 56, Chapter 18: College Physics
Uploaded: 2020-05-16T18:41:44-08:00
Duration: 5 min 24 s
Channel: Anna Zeng
Description: 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.

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.

Key Concepts

Transient Circuit Behavior

The behavior of circuits during sudden changes, such as when a switch is activated, is essential to creating a changing current. These transient events lead to variations in the magnetic field, which, according to Faraday's Law, generate an induced emf. This is crucial in designing circuits that rely on rapid changes to produce a significant induced voltage in a separate coil.

Mutual Inductance

Mutual inductance refers to the ability of a time-varying current in one coil to induce a voltage in a nearby coil through their shared magnetic field. This concept is critical when designing circuits where one coil (the primary) influences another coil (the secondary), even in the absence of a direct electrical connection.

Electromagnetic Induction

This is the phenomenon where a changing magnetic field produces an electromotive force (emf) in a nearby conductor. It underpins the operation of devices such as generators and transformers, and is the key principle allowing an emf to be induced in a coil that is not directly connected to the battery.

Faraday's Law of Induction

Faraday's Law quantifies electromagnetic induction by stating that the induced emf in a closed circuit is proportional to the negative rate of change of magnetic flux through the circuit. This principle provides the mathematical basis needed to show why the circuit, with its changing current and magnetic fields, will induce an emf in the separate coil.

Transcript

00:01 In this question, we are given a 12 -volt battery, some wires, a switch, and a separate coil of wire.

00:07 And we are to, according to part a, design a circuit that will produce an emf around the coil, even though it is not connected to the battery.

00:14 So i'm going to design something that also involves an iron core.

00:21 And i will explain the purpose of having this iron core in a bit.

00:27 So i'm going to name this the iron core.

00:29 All right.

00:31 So first i am going to wrap the wires that i'm given around one end of the iron core.

00:40 And of course i need to connect it to a battery source.

00:47 And i will also install the switch right here.

00:51 So this is the switch.

00:54 This is the battery.

00:59 And this is the wire that you're given.

01:02 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.

01:13 So this is a separate coil.

01:20 So how is it that we can induce an emf in this coil even though it is not directly connected to the battery? well, the moment you close the switch right here, what will happen is you will have now a running current within this primary coil right here.

01:43 So note, because you just close the switch, the current is not yet steady.

01:50 It is still increasing, even though it takes a very short time to get to a steady value...

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