### Video Transcript

In this video, we’re going to be looking at a device known as a moving coil galvanometer. The moving coil galvanometer is a fairly simple but very useful device, which is used to measure electrical currents. And it can be used to make ammeters, voltmeters, and ohmmeters, which are used to measure currents, voltages, and resistances in circuits. In this video, we’ll take a look at how moving coil galvanometers work and how we can calculate their sensitivity.

But first, let’s quickly take a look at what a moving coil galvanometer actually does. So here we have a simple circuit diagram. Over here is a moving coil galvanometer. And here it’s being connected in series with three components: a cell, a switch, and a resistor. The cell provides a potential difference so that a current will flow around the circuit when the switch is closed. The switch is just here so we can turn our circuit on and off. And we include a resistor in our circuit just so that the current produced by the cell doesn’t get too high.

Now, the use of a moving coil galvanometer in this circuit is that it will give us an indication of the magnitude and the direction of the current in the circuit. This galvanometer has a scale with zero in the middle. And when no current is flowing, such as in this case because the switch is open, the needle will point towards the zero. Allowing current to flow through the galvanometer in one direction will cause the needle to deflect one way. And allowing a current to flow in the opposite direction will cause the needle to deflect the other way. The total amount of deflection indicates the magnitude of the current, so let’s take a look at what happens when we close the switch.

Looking at our cell, we have a positive terminal on the left and a negative terminal on the right. This means that conventional current, which we can imagine as a flow of positive charge, is directed in the clockwise direction around the circuit. The current flows through the moving coil galvanometer, and this causes the needle to deflect by a certain amount. And charge will continue to flow around the circuit in a clockwise direction until it gets back to the cell, which completes the circuit. The needle on the galvanometer will stay in this position until we open the switch. The current stops flowing and the needle moves back to zero.

Now let’s see what happens if we flip this cell around. Now, when we close the switch, charge flows in the opposite direction around the circuit. And this time, we can see that the needle on the galvanometer has deflected by the same amount but in the opposite direction. So in this specific circuit, our galvanometer is measuring an anticlockwise current as negative and a clockwise current as positive. If we add another identical cell in series with the first one, we effectively double the size of the current in the circuit. And we would also see that the deflection of the needle on the galvanometer has doubled.

So this basically illustrates what a galvanometer does. By moving a needle across a dial, it indicates both the magnitude and the direction of the current flowing through it. So to see how this works, let’s take a look inside. At the core of a moving coil galvanometer is a cylinder of iron. This has a conducting rod attached to each end, although it’s important to note that these rods are electrically separate to the iron. So there’s a small piece of electrically insulating material here, which prevents electricity from being conducted between the rods and the iron.

We then have a piece of thin wire connected to the end of one of the conducting rods, which wraps around the iron cylinder before connecting to the rod at the other side. And in a real galvanometer, this coil of wire would have lots more windings. We then have two components known as torsional springs attached to the far ends of the conducting rods. These springs allow the conducting rods, the iron cylinder, and the coil of wire to rotate as a single piece. But they apply a torque in the opposite direction. The further the iron core and the coil are twisted, the more torque these springs apply, and so they prevent the core and the coil from spinning around.

The springs are made of conductive material and form an important part of the circuit. These ends of the springs act as the terminals of the galvanometer. The iron cylinder and the coil of wire are surrounded on both sides by the two poles of a large permanent magnet. Note that in this diagram, we haven’t drawn the entire magnet. We’ve only drawn the two polar pieces that we’re interested in. So let’s say in this case we have the north pole on the left and the south pole on the right. And the final components of our galvanometer are a needle connected to one of the conducting rods and a dial. So now, when the iron core and the coil of wire rotate, the needle will move across the dial.

So we now have a complete schematic of a moving coil galvanometer. And because there’s no current flowing through it at the moment, the needle is pointing to zero. As we mentioned before, the terminals of the galvanometer are here and here. Let’s say that this terminal is connected to the positive electrode of a cell, and this terminal is connected to the negative electrode. We know that conventional current refers to the flow of charge from positive to negative, which means the current in the galvanometer is in this direction. Charge flows along this torsional spring down the conducting rod and then around the loop of wire in this direction. Charge flows around all the windings of the coil before flowing down the other conducting rod. It then flows out of the galvanometer and back towards the negative electrode of the cell.

In order to understand how a moving coil galvanometer works, we just need to focus on the current within the coil of wire. Fundamentally, a moving coil galvanometer works on the same principle as an electric motor. This principle is known as the motor effect. Let’s recall that the motor effect is where a current-carrying wire at an angle to a magnetic field will experience a force. Looking at our diagram, we can see that we have a current in a coil of wire between two poles of a permanent magnet. In this diagram, we can see that we have the two poles of the magnet on the left and the right and that current is directed into and out of the screen. So it seems safe to say that our current-carrying wire is indeed at an angle to the magnetic field.

Now, magnetic fields point away from the north pole and towards the south pole. But within a moving coil galvanometer, we find that the magnetic field acts more or less radially as shown by these blue arrows. This is due to the effects of the iron core. The iron is easily magnetized, which means the magnetic field will preferentially pass through the core rather than through the air. This is important as it means the two longer sides of the coil of wire essentially experience a uniform magnetic field as they rotate.

We can see that the current in these long sides of the coil of wire both into and out of the screen is perpendicular to the magnetic field at that point. When this is the case, we can find the size of the force produced by the motor effect using the equation 𝐹 equals 𝐵𝐼𝑙, where 𝐹 is the magnitude of the force produced. 𝐵 is the magnitude of the magnetic field, 𝐼 is the magnitude of the current, and 𝑙 is the length of wire passing through the magnetic field.

It’s also possible to calculate the direction of the force. And this piece of information will help us understand how a moving coil galvanometer works. One of the ways we can do this is using Fleming’s left-hand rule. This is also known as the left-hand rule for motors, or sometimes just as the left-hand rule. If we extend the thumb, index finger, and middle finger of our left hand such that they’re all at right angles to each other, this can help us remember the direction of the resulting force when a current is at a right angle to a magnetic field.

Specifically, if our index finger is pointing in the direction of the magnetic field, which is usually represented by the symbol 𝐵, and our middle finger is pointing in the direction of conventional current flow, represented by the symbol 𝐼, then our thumb will now point in the direction of the resulting force on the current-carrying wire.

To work out how the coil in our galvanometer will behave, let’s consider one of the lengths of wire going into the screen on the right-hand side of the diagram. Looking at our diagram, we can see that the magnetic field lines intersecting this wire are going horizontally from left to right. And we’ve also worked out that the direction of conventional current in this section of wire is into the screen. So using the left-hand rule, if we point our middle finger into the screen and our index finger from left to right, then we find that our thumb is pointing straight down. This means that there’s a downward force acting on this part of the wire.

If we look at the length of wire on the other side of the diagram, we can see that the magnetic field here is also acting horizontally from left to right. But this time, the current is coming out of the screen. So using the left-hand rule again, if we position our middle finger so that it’s pointing out of the screen and we position our index finger so that it’s pointing from left to right, we find that now our thumb is pointing upwards, which means that this part of the wire experiences an upward force. So since we have an upward force acting on the left side of the loop and a downward force acting on the right side of the loop, we find that the core, the coil, and the conducting rods rotate in a clockwise direction. And this rotation causes the needle to deflect to the right.

It’s important to note that, unlike in an electric motor, these torsional springs oppose the motion of the core. In its current position, it isn’t moving, but it’s still experiencing a torque due to the motor effect. And this torque is exactly the same size as it was when the coil started to move. However, as the coil starts to rotate, the torsional springs start to produce a torque acting in the opposite direction. This torque gets bigger and bigger as the coil rotates further until eventually it’s exactly the same size as the torque due to the motor effect. The point at which these two counterrotational torques are in equilibrium is the point at which the needle eventually stops moving.

Now, if we were to increase the size of the current, then the electromagnetic force acting on the coil would increase, meaning the needle could deflect further before the torsional springs could provide sufficient force to stop it from turning. Or in simple terms, the larger the current in the galvanometer, the further the needle deflects. And if we were to reverse the direction of the current, we would find that the needle deflected in the opposite direction. In fact, moving coil galvanometers are constructed such that the deflection angle of the needle is exactly proportional to the current flowing through the galvanometer.

So if we say this current has a magnitude 𝐼 and we call the deflection angle of the needle 𝜃, then we can say that 𝜃 is proportional to 𝐼. We can turn this proportionality statement into an equation by introducing a constant of proportionality, which we’ll call 𝑘. This gives us the expression 𝜃 equals 𝐼𝑘. Now in this equation, 𝑘 is some constant which, when we multiply it by the current, tells us the deflection of the needle of our galvanometer. So if 𝑘 was very large, that would mean that a small value of 𝐼 would result in a large value of 𝜃. Conversely, if 𝑘 was very small, then even a large value of 𝐼 would result in a small value of 𝜃.

So we can think of this constant of proportionality as being the sensitivity of our galvanometer. The bigger the value of this constant, the bigger the deflection of the needle for a given current. In light of this, we can replace the symbol 𝑘 with a capital 𝑆 for sensitivity. If we now divide both sides of this equation by 𝐼, we’re left with the expression 𝑆 equals 𝜃 divided by 𝐼. In other words, if we have a current of magnitude 𝐼 in our galvanometer and this causes the needle to deflect by an angle of 𝜃, then the sensitivity of our galvanometer is simply the angle divided by the current. In fact, the sensitivity of our galvanometer can be defined by the change in the angle of deflection of the needle, Δ𝜃, divided by the change in the current flowing through the galvanometer, Δ𝐼.

Since the sensitivity is given by dividing an angle by a current, we can express it in units of degrees per amp or radians per amp, although given that one amp is a relatively large current, we might instead use milliamps or even microamps in our units. So we’ve now seen how a moving coil galvanometer is constructed. We’ve described the physical principles that underlie its operation. And we’ve looked at how we can mathematically describe the deflection of the needle in relation to the sensitivity of the galvanometer and the magnitude of the current within it.

Let’s now recap the key points that we’ve looked at in this video. Firstly, we’ve seen that a moving coil galvanometer is an electromechanical device used to detect and indicate an electric current. We’ve seen the components that make up a moving coil galvanometer, including a coil of wire within a magnetic field. Current flowing in the coil causes it to rotate due to the motor effect, and this in turn causes a needle to deflect across a dial, which indicates the current. Galvanometers with a zero in the center of the dial, like the ones we’ve looked at in this video, are capable of indicating the direction of the current. And finally, we’ve seen that the sensitivity of a galvanometer is given by 𝑆 equals Δ𝜃 over Δ𝐼. This is a summary of the moving coil galvanometer.