The diagram shows a Coolidge tube used for the production of X-rays. Which of the potential differences 𝑉 one and 𝑉 two would have the greater voltage? (A) 𝑉 one, (B) 𝑉 two, (C) either potential difference could have the greater voltage, or (D) both potential differences have the same voltage.
Let’s start by looking at the potential difference 𝑉 one. 𝑉 one is responsible for creating a charge difference across the components within the Coolidge tube, the negatively charged cathode coil and the positively charged anode target. This difference in charge causes electrons from the cathode coil to accelerate towards the anode target. And when an electron impacts the target, an X-ray photon is produced. How quickly these electrons are accelerated through the tube depends on the potential difference 𝑉 one, which is why 𝑉 one is often called the acceleration potential difference, because it determines the acceleration of these electrons.
𝑉 two, on the other hand, only supplies the potential difference across the cathode coil. Its purpose is not to increase the acceleration of the electrons like 𝑉 one, but rather to provide power to the cathode coil. This is because when the cathode coil is supplied power, it begins to heat up to very high temperatures and begins a process called thermionic emission, in which the electrons present within the cathode coil begin to escape. For this reason, the potential difference 𝑉 two is often called the thermionic potential difference because it is responsible for causing thermionic emission from the cathode coil.
Now that we know what 𝑉 one and 𝑉 two are used for, let’s look at their typical values. 𝑉 one is responsible for the acceleration of the electrons in the Coolidge tube, meaning that a higher 𝑉 one means a higher acceleration of the electrons, meaning that higher-energy X-ray photons are also produced. When we use a Coolidge tube, it is because we want these high-energy X-ray photons, which means that we want a high potential difference, very high, often in the thousands or tens of thousands of volts.
Looking at 𝑉 two, we know that it only supplies power to the cathode coil. A higher thermionic potential difference allows more electrons to escape from the coil. But actually, most of the time we don’t need that many. And so the thermionic potential difference is usually nine, 12, or 15 volts, rarely breaking 100. So we say it is tens of volts. So 𝑉 one, the acceleration potential difference, will almost always have the greater voltage. But these are just how it tends to be and for a good reason. Answer (C) says that either potential difference could have a greater voltage, and this could be true. And the same with answer (D) as well, they could potentially have the same voltage.
But doing either of those things wouldn’t really accomplish much. If 𝑉 one was shrunk down to the tens of volts, like 𝑉 two, then the acceleration of the electrons in the Coolidge tube would be almost nonexistent. The X-ray photons that would be produced would be so low energy they would be very difficult or almost impossible to detect. The opposite scenario where we boost up 𝑉 two to thousands or tens of thousands of volts is simply very dangerous. Depending on the composition of the cathode coil, it could simply melt into the bottom of the tube, or it could explode, both of which would irreparably damage it.
For these reasons, the answer to “Which of the potential differences 𝑉 one and 𝑉 two would have the greater voltage?” is (A) 𝑉 one, the acceleration potential difference.