Video Transcript
A galvanometer and a resistor are connected in series in an incorrect attempt to form an ammeter. Which of the following best explains the effect of connecting the resistor in series? (A) The maximum current measurable by the ammeter is less than the maximum current measurable by the galvanometer. (B) The current measured by the ammeter is greater than the actual current. (C) The current measured by the ammeter is less than the actual current.
In our question, we’re told that a galvanometer and a resistor are connected in series. Using circuit symbols, that would look like this. We’re told that this arrangement is an incorrect attempt to form an ammeter from these two components. We want to choose which of our answer options best explains what happens when the galvanometer and resistor are connected this way. The first thing we can note is that when our answer options talk about an ammeter, that term is describing this arrangement of components. We know that this is an incorrect arrangement of these components to form an ammeter. But for now, we’re thinking of an ammeter as a galvanometer and resistor connected in series.
What we’re calling our ammeter, boxed here in orange, is part of a larger circuit. We’ll say that that circuit consists of a voltage supply and some resistance. In this series circuit, some current, we’ll call it 𝐼, exists all throughout the circuit. The purpose of an ammeter is to measure this current. And at this point, let’s recall that the correct way to arrange a resistor and a galvanometer so that they really do form an ammeter is in parallel like this. The reason for this arrangement is the measurement scale of a galvanometer tends to be relatively small. What we mean by that is if this were the measurement display of the galvanometer, only a relatively small current is needed to maximally deflect the measurement arm of the galvanometer.
Any current of greater magnitude than this can’t accurately be measured by the galvanometer. This challenge of the limit of the galvanometer’s measurement range is overcome when we arrange the galvanometer in parallel with a relatively low-resistance resistor. That way, most of the current in the circuit passes through the branch with a resistor rather than the one with the galvanometer. In this way, we don’t overwhelm the galvanometer’s measurement capability. When we arrange a galvanometer in series with a resistor though, there is no such safeguard against exceeding the galvanometer’s measurement range.
Even for normal amounts of current 𝐼 in a circuit then, we would probably see a display like this if we looked at our galvanometer’s reading, indicating potentially that the magnitude of current in the circuit was greater than the galvanometer can measure. Here, we’re calling this reading by the galvanometer the current measured by our ammeter. As we’ve seen, this is likely not the actual current in the circuit but instead is just the greatest current that our galvanometer is capable of measuring. This situation is described by answer choice (C) that the current measured by the ammeter, in this case this current, is less than the actual current in the circuit.
Answer option (A) says that the maximum current measurable by the ammeter — recall that here we’re talking about a galvanometer and resistor in series as an ammeter — is less, option (A) says, than the maximum current measurable by the galvanometer. Based on our sketch though, we see that those values are actually one and the same. We won’t choose answer choice (A). And answer choice (B) says that the current measured by the ammeter, again our galvanometer and resistor in series, is greater than the actual current. We’ve seen though that actually our galvanometer arranged this way gives an under indication of the current in the circuit rather than an over indication.
Our answer then is option (C). When a galvanometer and a resistor are connected in series to form an ammeter, the current measured by the ammeter is less than the actual current.
