Video: Eq17S1-Physics-Q10B

What is the function of the shunt resistance in an ammeter?


Video Transcript

What is the function of the shunt resistance in an ammeter?

Imagine that we have a simple circuit consisting of a cell supplying voltage, a resistor, and an ammeter to measure current in the circuit. The way our circuit is set up right now 100 percent, all of the current in the circuit will move through the ammeter by necessity. And like any measurement device, this ammeter has an upper limit, in this case, an upper limit on the amount of current that it’s able to handle, that it’s able to let pass through. Over this range, the ammeter is able to make very precise measurements of the amount of current in the circuit.

That being said, an idea was developed to extend the range of measurable current values. Here’s the idea. What if we put another resistor in parallel with our ammeter. And not only that, but we make the value of this resistor fairly low compared to the internal resistance of the ammeter. If we do this, then when current moves through this circuit and reaches this parallel branch, at this point the great majority of the current will go to the branch of this circuit that has less resistance. And a very small fraction of the overall current will go through the ammeter.

In this way, we’re able to ensure that our ammeter isn’t given more current than it can handle. And yet the overall current in our circuit faces no such limitation, since the great majority of it is shunted away from the ammeter. That current which goes through the branch we’ve just drawn in the circuit goes through what is called a shunt resistor. We’ll call it 𝑅 sub S. True to its name, the function of a shunt resistor is to draw away most of the circuit current from the ammeter itself. Now, we might think, well, doesn’t that defeat the purpose of an ammeter? Because if current is not moving through it, then how can we measure it?

Well, through some clever design, we actually are able to still measure the overall circuit current, even when most of it doesn’t travel directly through the ammeter. That’s because the resistance of our shunt resistor 𝑅 sub S and the internal resistance of the ammeter are carefully coordinated one with another. Here’s an example of how that could work. If we put a shunt resistor in our circuit with a value of one ohm, knowing that the resistance of our ammeter was 100 ohms, then because of the way that electrical current prefers to flow through parallel branches that have less resistance, we could say that the current through the shunt resistor is 100 out of 101 parts of the total current in our circuit while the current through the ammeter is one one hundredth [one one hundred and oneth] of that.

In other words, so long as we’re able to measure the current through our ammeter and we know the relationship between the resistance of the ammeter and the resistance of the shunt resistor, then we’re still able to know the overall total current in our circuit. So that’s one function of a shunt resistor to increase the range of measurable current in a circuit. But if we look at the shunt resistor in the circuit diagram, we see it has another effect. Remember that we said that the ammeter itself has its own internal resistance value. The resistance of this device isn’t zero. So by adding in our shunt resistor 𝑅 sub S, we now have two resistors arranged in parallel.

Now if we had two resistors, we can call them 𝑅 one and 𝑅 two arranged in parallel with one another. What can we say is true about the overall resistance of this parallel branch? We can recall a relationship for the equivalent resistance of two resistors arranged in parallel. We’ll call it 𝑅 sub eq. This equation tells us that if we were to take two resistors arranged in parallel and rewrite them as a simplified single resistor and equivalent resistance, the value of that equivalent resistance would be the product of 𝑅 one and 𝑅 two divided by their sum. We can consider for a moment just how 𝑅 sub eq, the equivalent resistance, compares to 𝑅 one and 𝑅 two.

Algebraically, we can rewrite this equation as follows. 𝑅 sub eq is equal to 𝑅 one multiplied by the quantity 𝑅 two divided by 𝑅 one plus 𝑅 two. Now, let’s look at this term in parentheses. Is this term bigger or less than one? If we assume that 𝑅 one and 𝑅 two are both greater than zero, that is, they have nonzero resistances, then this overall fraction must be less than one because we’re dividing a smaller number by a larger number. We can, therefore, conclude that 𝑅 sub eq, the equivalent resistance of combining these two resistors, is less than the value of 𝑅 one by itself.

But notice something interesting. When we rewrote our equation for 𝑅 sub eq, we could just as easily have factored out the 𝑅 two from outside a set of parentheses. That is, we could have written it this way. 𝑅 sub eq is equal to 𝑅 two times the quantity 𝑅 one over 𝑅 one plus 𝑅 two. And once again, the quantity in parentheses is less than one because we divide a smaller number by a larger number. We can conclude from that the equivalent resistance is also less than 𝑅 two, the other resistor in parallel. Overall then, we’re finding that when we combine two resistors in parallel, the equivalent or effective resistance of those two is less than either of the resistors individually.

We can say that this is also part of the function of the shunt resistance in an ammeter where when we add our shunt resistance, we consider that a part of our overall current measurement device. We saw before that when we add the shunt resistance into our ammeter, it increases the range of measure current possible in the circuit. But then we also saw how this edition impacted the overall resistance of the ammeter. We found that adding a shunt resistor also decreases the overall ammeter resistance. Either one of these answers describes the function of the shunt resistance.

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