# Lesson Video: Alternating-Current Ammeters Physics

In this video, we will learn how to describe the construction of ammeters using the thermal expansion of conducting wires to measure alternating currents.

13:22

### Video Transcript

In this video, we’ll be looking at alternating-current ammeters. These are devices which we can use to measure the size of a current in an alternating-current or AC circuit. Specifically, we’ll be looking at a type of AC ammeters known as a hot-wire ammeter. We’ll look at all the components that make up a hot-wire ammeter. And we’ll look at how these components function together to measure current. Now measuring the size of an alternating current, which is a current that repeatedly changes direction, is a bit more complicated than measuring a direct current, which is a current that just goes in one direction. So to start off with, let’s remind ourselves of how a direct-current ammeter works and talk about why this isn’t suitable for measuring an alternating current.

So here, we have a simple series circuit containing a cell, which is a direct current source and a resistor. And we can see that a direct-current ammeter has been connected in series to measure the current in the circuit. Now, if we were to open this ammeter up and have a look inside, we’d see that this is a type of ammeter known as a moving coil ammeter consisting of a galvanometer and a shunt resistor wired in parallel to each other. A galvanometer is a device which uses electromagnetism, specifically the motor effect, to move a needle across a dial and indicate both the size and direction of a current within it. Now this type of ammeter works really well for measuring constant direct currents, like the one we have in this circuit. However, if we replace our direct-current source with an alternating-current source, we’d quickly see that this type of ammeter isn’t very useful.

Now, even though galvanometers can indicate the current in either direction — for example, an anticlockwise current in our circuit might cause the needle to deflect to the left, meaning a clockwise current would cause the needle to deflect to the right — this type of ammeter is still not very useful for measuring alternating currents. The reason for this is that both the magnitude and direction of an alternating current are changing constantly. This means that the needle on the galvanometer would oscillate back and forth, which makes it difficult to read. Furthermore, because of the inertia of the needle and the moving components within a galvanometer, the needle would only be able to keep up with very low-frequency alternating currents. So a moving coil ammeter is a very limited use for measuring alternating currents.

To do this, we need to use a radically different ammeter design. And one such design is known as the hot-wire ammeter. So here’s the same circuit, but this time we have a hot-wire ammeter attached instead of a moving coil ammeter. Let’s now change our circuit diagram to show what’s inside this ammeter. Okay, so there’s a lot going on here. And this diagram is kind of unusual because everything on the left of this dashed line is a standard circuit diagram. But everything to the right of this dashed line is not a circuit diagram. Instead, we have things like a spring, a pulley, and a piece of string. And we’ll look more at these components in a minute. But for now, let’s focus on this part of the diagram.

Here, at least we can see that the design bears some resemblance to a moving coil ammeter in that the wire coming from an alternating-current source splits into two parallel branches. And just as with the moving coil ammeter design, one of these branches contains a shunt resistor. As is usually the case with the shunt resistor, its function is to ensure that a certain amount of the current occupies this part of the circuit, thus ensuring that only a certain fraction of the total current produced by our alternating-current source passes down the other parallel branch. One obvious difference we can see from the moving coil ammeter is that in a hot-wire ammeter, there’s no galvanometer.

We instead have a specific length of wire made from a carefully chosen material. Usually this is made of a platinum-iridium alloy, which just means it’s a mixture of the two metals, platinum and iridium. This wire is an electrical conductor. And it’s important to remember that it has a certain resistance, even though we haven’t drawn the circuit diagram symbol for a resistor. This wire forms an important part of the circuit, but everything to the right of this wire in our diagram is not part of the circuit. This means that no charge flows through any of these parts. Instead, these parts have a mechanical function.

Shown in red is a piece of silk string. One end of the string is attached to the platinum-iridium wire and then passes over a pulley. And the other end of it is attached to a spring. The other end of the spring is fixed. And the spring is always stretched so that it applies a tension to the string and, in turn, to the platinum-iridium wire. Finally, we have a needle attached to the pulley, which moves across the dial as the pulley rotates. And that’s everything that makes up a hot-wire ammeter.

So what exactly does all of this stuff do? Well, first of all, our alternating-current source sets up an alternating current in the circuit. This means that charge flows in one direction and then the other. In the parallel branches of our circuit, charge flows in this direction, passing downward through the shunt resistor and the platinum-iridium wire and then back in the opposite direction. Now, when charge flows through a resistor, some electrical energy is converted into thermal energy. So this means that the shunt resistor heats up. But crucially, so does the platinum-iridium wire because it, too, has a resistance.

This resistive dissipation in the platinum-iridium wire means that it heats up. And as it heats up, it undergoes thermal expansion and gets longer. Because this wire is under tension from the silk string and the spring, as it expands, the string is pulled over the surface of the pulley, causing the pulley to rotate and the needle to move across the dial. So when there’s a current in the circuit, the needle deflects. In fact, the higher the current in the wire, the more the needle deflects. This is because the amount of heat produced by the platinum-iridium wire in a given amount of time is proportional to the square of the current, as represented by this expression, where 𝑄 is the heat produced and 𝐼 is the current.

This means that if we increase the size of the current produced by our alternating-current source, then the rate at which heat is produced by the platinum-iridium alloy wire will also increase. As the temperature of this wire increases, the amount of heat it gives away to its surroundings also increases. This means that for a given size of alternating current 𝐼, the wire will quickly reach a temperature where the amount of thermal energy generated in it is equal to the amount of heat it gives away. We can say that the wire reaches thermal equilibrium with its surroundings, and at this point its temperature remains constant. If the temperature of the platinum-iridium wire stays constant, then the amount it has expanded by also stays constant, which means that we get a constant amount of deflection of the needle across the dial.

If we were to now increase the size of the alternating current in our circuit, then the amount of heat produced by the wire would increase further, causing the wire to reach thermal equilibrium at a higher temperature that’s expanding slightly more and increasing the deflection of the needle. And this is the basis by which our hot-wire ammeter functions. One important thing to note about this type of ammeter is that the scale on the dial is nonlinear. This is due to the fact that the heat produced in the wire is proportional to the current squared. This means that if we were to increase the size of the alternating current at a constant rate, the amount of heat produced by the wire would increase at an increasing rate.

This means that at low currents, a current increase of, say, one amp would cause a relatively small movement of the needle. But if we increase the size of the current by one amp again, this has a bigger effect on the amount of heat produced by the wire and thus causes a bigger movement of the needle. The result is that equal-sized increments of current have bigger and bigger gaps between them on the dial as the current increases. Okay, so now that we’ve seen how a hot-wire ammeter works, let’s try answering a practice question.

The platinum-iridium alloy wire in a hot-wire ammeter expands when its temperature increases and contracts when its temperature decreases. The temperature of the wire is dependent on the current in the wire. A hot-wire ammeter using such a wire will give a constant reading for an alternating current that has a particular peak value. Which of the following most correctly explains how an alternating current with a frequency of 50 hertz in the wire can produce a constant hot-wire ammeter reading? (A) The wire heats a hot-wire ammeter’s other mechanical components. The expansion and contraction of these components are out of phase with each other, so the reading on the ammeter remains constant. (B) The wire expands when its temperature increases much faster than it contracts when its temperature decreases, so the wire never reduces in temperature for a sufficient time to contract noticeably. Or (C) the frequency at which the wire can undergo a cycle of expansion and contraction is much smaller than the frequency of the alternating current, so the expansion of the wire corresponds to the effective value of the current.

So this question is asking us to identify the correct reason that a hot-wire ammeter displays a constant reading in response to an alternating current. Let’s clear the answer options off the screen for now so we can have a closer look at how this works. To start with, let’s recall that an alternating current is a current whose direction and magnitude are constantly changing. We can draw a graph with current on the vertical axis and time on the horizontal axis that shows how an alternating current varies over time.

Initially, at time zero, there’s zero current. After this, we can see that current increases up to some maximum value before decreasing again back down to zero. After this, the current increases in the negative direction up to some maximum negative value. This represents current going in the opposite direction. The magnitude of this current then decreases to zero again. And this cycle then repeats over and over again, with the current increasing in one direction and then decreasing again, then increasing in the opposite direction and decreasing again, and so on.

In this question, we’re dealing with an alternating current with a frequency of 50 hertz. This means that the current undergoes one full cycle like this 50 times per second, meaning that the current changes direction 100 times every second. Now, attempting to measure the size of a current like this is much more challenging than measuring that of a direct current, which is one that stays at a constant level in one direction. To measure a direct current, it’s common to use a device known as a moving coil ammeter, which is based on a galvanometer. In a galvanometer, the magnetic field produced by a current causes a needle to defect across a dial by an amount proportional to the size of the current. This works great for direct currents. However, it doesn’t work so well for alternating currents. This is because a galvanometer effectively measures the magnetic field produced by a current.

And if the current is rapidly alternating, then the magnetic field will alternate at the same frequency. This means if we connect our galvanometer to an alternating current source, we find that the needle fluctuates rapidly from side to side, which makes it essentially impossible to obtain an accurate reading. In contrast, a hot-wire ammeter, like the one mentioned in this question, is an ammeter which is designed specifically to measure the size of alternating currents. The way it does this is rather than looking at the electromagnetic effects of a current like a galvanometer does. It measures the thermal effects of charge flowing in a wire.

A hot-wire ammeter can measure the alternating current in a circuit by allowing a fraction of this current to flow along a platinum-iridium alloy wire. Attached to this wire is a silk thread which passes over a pulley, which is then attached to a spring which keeps it under tension. The pulley then has a needle attached to it, which points to a dial. The way that this works is that platinum-iridium wire produces heat when charge flows through it due to resistive dissipation. Although some of this heat is given away to its surroundings through conduction and radiation, the temperature of the wire itself increases, causing it to undergo thermal expansion. As the temperature of the wire increases, the rate at which it transfers heat to its surroundings also increases, until eventually it equals the rate at which the wire dissipates electrical energy. At this point, the temperature of the wire stops increasing.

Now this is where things get interesting. As it mentions in the question, the temperature of the wire is dependent on the current in the wire. However, we know that the current in the wire is rapidly alternating. So why is it then that the temperature of this wire doesn’t fluctuate too? Well, simply put, the thermal expansion and contraction of this wire is much slower than the alternation of the current. In a given period of time, the heat produced by the wire 𝑄 is proportional to the current squared. So it is technically true that the wire produces more heat when the magnitude of the current is at its maximum, which corresponds to these positions on the graph.

However, the overall temperature of the wire, as well as its thermal contraction and expansion effects, change so slowly that there’s no time for the wire to cool down and contract between these two points of maximum current magnitude. This means that for a current with a given peak value, a hot-wire ammeter will give a constant reading. So now, if we look back at our answer options, we can see that this is best described by option (C). An alternating current with a frequency of 50 hertz can produce a constant hot-wire ammeter reading because the frequency at which the wire can undergo a full cycle of expansion and contraction is much smaller than the frequency of the alternating current. So the expansion of the wire corresponds to the effective value of the current.

Let’s now review some of the key points that we’ve learned in this lesson. We’ve seen that a hot-wire ammeter uses resistive dissipation in a platinum-iridium alloy wire to measure alternating currents. The platinum-iridium alloy wire is connected in parallel with a shunt resistor, and alternating current in the wire causes its temperature to increase. Thermal expansion of the platinum-iridium alloy wire is measured using a spring, a silk string, a pulley, and a needle on a dial. And the amount of thermal expansion corresponds to the effective value of the current. This is a summary of alternating-current ammeters.