Describe two functions of the shunt resistor found in ammeters.
To get a sense for what these functions might be, let’s imagine we have an ammeter, a device to measure current, positioned in series in a closed circuit. This ammeter, we’ll say, does not have a shunt resistor. In that case, this means that 100 percent of the current that moves through the circuit must pass through the ammeter. Normally, this is a good thing for a device designed to measure current.
But what if the amount of current in this circuit exceeds the upper limit of the ammeter’s ability to measure? In response to this, we can add a parallel branch to our circuit with another resistor called the shunt resistor. We’ll now consider this resistor part of the ammeter device itself.
This addition of our ammeter changes it from a series to a parallel device. If we call the original resistance of our ammeter 𝑅 sub 𝐴, we can then write that the final resistance of our ammeter, 𝑅 sub 𝐹, which includes the shunt resistor branch, is equal to 𝑅 sub 𝑆 times 𝑅 sub 𝐴 over 𝑅 sub 𝑆 plus 𝑅 sub 𝐴. We know that, mathematically, 𝑅 sub 𝐹 must be less than either 𝑅 sub 𝑆 or 𝑅 sub 𝐴. That is, the overall resistance of our ammeter has decreased with the addition of a shunt resistor. So that’s one function of the shunt resistor: it decreases the resistance of the ammeter.
We can also recall the reason for adding the shunt resistor in the first place. It was because our ammeter was being overwhelmed by current, so we needed to put in a parallel branch that would divide current over two different resistors. Doing this increases the maximum current values we’re able to measure with this ammeter. And this is another function of the shunt resistor: to increase the range of measurement of the ammeter.
That gives us two functions for the shunt resistor, but we can think of one more. In order to spare the original ammeter resistor as much current as possible, 𝑅 sub 𝑆, the value of the shunt resistor, is often deliberately made very low. That means that much more current will move through this parallel branch in the shunt resistor than through the original ammeter itself. This means that another function of the shunt resistor is to carry a majority of current in the ammeter. This gives us not just two but three functions of the shunt resistors found in ammeters.