Jim has taught undergraduate engineering courses and has a master's degree in mechanical engineering.
Every day, we make use of a special case of electromagnetic induction known as mutual induction. In this lesson, we'll talk about this special phenomenon and how it is used in many common devices.
Using a shared magnetic field, one coil transfers power to another.
Have you ever seen a power transformer on a utility pole? Or how about an AC adapter? Maybe you've used a transponder car key, or even an electric toothbrush? Either way, I'll bet you answered 'yes' to at least one of these questions, which makes an important point. We use a phenomenon known as mutual inductance on a daily basis without even knowing it. We're going to explore mutual inductance in greater detail so that we can understand how it is used in all sorts of everyday devices.
The ability of one current-carrying conductor to induce a voltage in another conductor through a mutual magnetic field is known as mutual inductance. When an alternating electric current flows through a wire, it creates an alternating magnetic field around the wire. If we wrap this wire into the shape of a coil, we can concentrate the magnetic field into the coil's center and make it much stronger. We'll call this the primary coil. Now, if we were to bring a secondary coil of wire with the same number of turns into close proximity, the alternating magnetic field would induce a voltage approximately equal to that in the primary coil.
At this point, you might be wondering why we would go through so much effort just to get the same voltage in both coils. One reason is that the coils don't have to be physically connected to transfer energy. This has some useful applications that we'll look at a bit later. Another reason is that we can achieve a different voltage in the secondary coil simply by changing the number of turns.
For example, if the secondary coil has twice as many turns as the primary coil, then the induced voltage will be twice as large. On the other hand, if the secondary coil has half the number of turns as the primary coil, the induced voltage will be half. As we can see, the voltage ratio between the two coils is the same as the turns ratio. The device that we've described here is called a transformer because it transforms one voltage into another voltage.
Current and voltage are inversely related.
Getting a higher voltage out of a transformer than what we put in may seem like we're getting something for nothing, but we need to look at what happens to the current and power as well. When it comes to transformers, voltage and current are inversely related. In other words, if the secondary voltage is twice as much as the primary voltage, then the secondary current will be half as much as the primary current.
Because of this relationship, power, which is the product of current and voltage, is the same going into and out of the transformer. In a way, a transformer is similar to a lever used to move a really heavy object. While your small force at one end gets turned into a big force at the other end, your large movement also gets reduced to a small movement by the same amount. In the natural world, there is always a trade-off that keeps us from getting something for nothing.
In order for mutual inductance to take place, the magnetic field must always be changing. At the beginning of our discussion, we specified that the primary coil of our transformer was connected to an alternating current source, which produced an alternating magnetic field. If, instead, we connected the primary coil to a direct current source, such as a battery, the magnetic field would be constant and unchanging. Since an unchanging field cannot induce a voltage in the secondary coil, transformers do not work with direct current. Alternating current is much better suited for use with transformers, which is a big reason why it is used for long distance power transmission, as we'll talk about next.
Applications of Mutual Inductance
Between a power plant and your home, the voltage must be adjusted inside of transformers.
Transformers are one of the most important applications of mutual inductance and can be found both outside and inside your home. Let's look at how they're used to send electricity from the power plant to your home. To minimize power loss in the long transmission lines, it is necessary to transmit the electricity at very high voltages, often in excess of 700,000 volts! The generators in the power plant generate much lower voltages, so the electricity has to be sent through a step-up transformer before it can be sent out to your house.
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A step-up transformer simply has more turns in the secondary coil than in the primary coil, so the output voltage is higher. Once the electricity gets near your home, it is sent through a series of step-down transformers so that you don't have 700,000 volts coming out of the electrical sockets in your home. As you may have guessed, a step-down transformer has more turns of wire in the primary coil than in the secondary coil, which results in a lower output voltage. Inside our homes, we often use additional step-down transformers to provide the lower voltages needed by most of our electronic devices.
Another important application of mutual inductance is to power devices without a physical connection. Wireless battery chargers are often used to charge small bathroom electronics, such as toothbrushes and shavers, because there are no exposed contacts that could cause a shock around water. The charging base contains the primary coil, which produces a varying magnetic field, and the battery pack contains the secondary coil, which charges the batteries with the induced voltage.
A diagram of the two coils in an electric toothbrush that work off of the same magnetic field.
Some devices are powered through mutual inductance either because they're too small for batteries or so you never need to change the battery. For example, most car keys contain a small transponder that is part of the car's anti-theft system. When the key is inserted into the ignition, a nearby primary coil in the dashboard pulses a magnetic field that induces a voltage in a secondary coil in the head of the key. The voltage powers a microchip, which transmits a signal to the car that allows the engine to start. Using mutual induction allows the key to be powered remotely, without the need for batteries.
Mutual inductance is the ability of a current-carrying conductor to induce a voltage in another conductor through a mutual magnetic field. Mutual inductance allows us to transmit electrical energy without physical contact between the conductors.
It also allows one voltage to be transformed to another voltage in a device known as a transformer. Inside this device, the primary coil, connected to an alternating current source, induces a voltage in the secondary coil. The voltage ratio between the primary and secondary coils is equal to the ratio of the turns in each coil.
The current is inversely related to the voltage, so that power going into the transformer is the same as the power leaving the transformer. Direct current does not produce a varying magnetic field and, therefore, does not work with transformers. This is a significant reason why alternating current is used for long distance power transmission.
Associated Definitions & Terms
ability of a current-carrying conductor to induce a voltage in another conductor
a device that houses the primary coil that is connected to the alternating current source
is equal to the ratio of turns in the primary and secondary coils
inversely related; the power going into a transformer is the same power leaving it
An understanding of this lesson will enable you to accurately do the following:
Define mutual induction
Outline the need for transformers to carry the power current
Calculate the voltage ratio based on the number of turns in the coils on one side or the other
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