 Let's introduce the idea of current sensitivity of a galvanometer and see why we should care about that. In a previous video, we built a moving coil galvanometer and the whole idea was when you pass some current through the coil, this current coil behaves like a tiny magnet and tiny magnets inside external magnetic fields experience a torque making this coil twist. And this is the expression that we found for this torque. The important thing over here was this angle between the magnetic moment and the external magnetic field will always be 90 degrees at any position. It's 90 degrees over here, 90 degrees over here, 90 degrees over here will always stay 90 degrees because the field is radio. And at the same time, we have coil springs which don't like to get twisted. So as they get twisted, they try to untwist producing a counter torque in the opposite direction. And this counter torque is found to be proportional to the angle through which this coil twists. And at equilibrium, the two torques are exactly equal to each other. And as a result, we see that the twist produced is proportional to the current giving us a linear galvanometer, exactly what we want. And if you need a refresher on this, feel free to go back our previous video on moving coil galvanometers. We have talked about this in great detail. But now let's rearrange this equation to give us phi, the deflection, divided by the current i. If I rearrange this, we will end up with, on the right hand side, we'll have this N A times B divided by the C, the spring constant. And now this term, let me keep it to the right. This term is what we call the current sensitivity of a galvanometer. Let's see why and let's see what it means. First of all, look at the units of this. Because there is a deflection on the numerator and current in the denominator, the unit becomes ampere, sorry, degrees per ampere. So let's take some values. Imagine in our galvanometer, this value was a thousand degrees per ampere. Then what does that mean? Well, that would mean that if you were to put one amp of current through this coil, it would tend to produce a deflection of a thousand degrees. And can you imagine thousand degrees like it tends to produce three turns, which is just not possible. It gets stuck somewhere, which means this galvanometer cannot handle one ampere. Something will break over here, which means we say that this is a very sensitive galvanometer. So we have high sensitivity, high sensitivity, which means you use this galvanometer to measure very small current. So maybe use this to measure milliamps of currents or hundreds, tens of milliamps of current. So measure small currents, measure small currents. On the other hand, what if this value was low? Maybe say 0.1 degree per ampere. What does this mean? Well, this would mean now if you put one amp of current, you get a very tiny amount of deflection. So it's not very sensitive to current. So you can use this to measure a lot of current. Let's say about hundreds of amps of current. So this is low sensitivity. So this is low sensitivity and use this to measure high currents, measure high currents. So clearly this number tells us how sensitive the output of the galvanometer, the deflection of the galvanometer is to the input current. So high sensitivity is kind of like when I was a child, when somebody would say a little bit of mean things to me, I would just cry out loud, very high output, very, very sensitive. And low sensitivity is like how I'm right now, a little bit mature. And so even if you tell a lot of mean things to me, I won't produce a lot of output. I'm very less sensitive to mean things now. And so different applications would require different sensitivity values. And that brings us to the question, how do we control the sensitivity of our galvanometer now? And for that, we look on the right hand side. So if you increase these, the sensitivity tends to increase. On the other hand, if you increase this, the sensitivity would tend to decrease. Let's see why. Well, if you increase the number of turns or the area of this coil or the magnetic field strength by producing say stronger magnets, in all these cases, the torque that is produced tends to increase. Think about it. The torque given due to a current tends to increase you to these values. And if the torque tends to increase, you tend to get more deflection, more output. And as a result, you tend to get more sensitivity. Some makes sense. On the other hand, what happens when you increase the value of C? What is the C again? Remember, C is the spring constant. Think of it as it tells you how stiff the spring is. So if you increase the value of C, you are making the spring stiffer. If you make the spring stiffer, it tends to generate a large counter torque, which means it will not allow a lot of output, it will not allow a lot of deflection. And that means it tend to decrease the sensitivity. So by controlling these values, you can get whatever sensitivity you want. Now let's see if we can apply this in a numerical. So let's keep this formula at the side and here is a numerical. Why don't you pause the video, read this thing and see if you can try and answer this question yourself first. All right. What I'll do is I'll color code things so we can understand what is what. So here's my color coded version. We are given a galvanometer has a coil of area. So its area is given, the number of turns is given to us, its magnetic field is given. We're also given what the spring constant is and we are given what the maximum deflection a galvanometer can accommodate. So that's the maximum deflection is given to us. We need to find what the maximum current that can be measured. So what I'll do is I'll first calculate what the current sensitivity is and let's see what that number tells us. And from that, let's see if we can figure this out. So let's calculate the current sensitivity. The current sensitivity 5 divided by i happens to be number of turns, which is 500 times the coil area, which is three times 10 to the power minus four. And everything is in SI units, we need to take care of the units times the magnetic field, which is 0.01 divided by C, which is the spring constant, 10 to the power minus five. And so what will I get if I put all of this? Well, let's see the zeros and the zeros cancel over here. I mean the decimals cancel. I get five, five threes are 15 and this will give me 110 on the top. And so I get 150. So I get 150 and what is units? Degrees per ampere. So I get degrees per ampere. You might have a question. How do we know it's a degrees or radiance? That's a good question. Well, here notice in the spring constant, it's given 10 to the power minus five and Newton meters per degree. So that tells me that this is in degrees. Okay. So what is the meaning of this? This means in our galvanometer, if I send one amp of current, the deflection we get is 150 degrees. That's a pretty large deflection. But now we are given that the maximum deflection that the galvanometer can accommodate is only 30. It cannot accommodate more than that. So what's the max current? So clearly if it can only accommodate 30, it will not be able to, we will not be able to send one amp of current through it. So the question then is, what is the maximum current that we can send? And I think we can just do this logically. I know that if I send one amp of current, one amp of current, I get a deflection of 150 degrees. But I know that the maximum deflection I can get is 30 degrees. So for 30 degrees, how many amps of current can I send? And remember, the only reason I can do that is because our galvanometer is linear. It's a linear device and that's why I can do this cross multiplication. And so if I do that, I get, what do I get? I get the maximum current to be 30 divided by 150. And that's 1 over 5, and that's 0.2 amperes. So our galvanometer can only handle the max of 0.2 amperes of current. So we can say that the range of our galvanometer is from 0 to 0.2 amperes. So I can change my sticker now and put amperes, and then this becomes an ammeter which can measure between 0 to 0.2 amperes.