QuestionJune 4, 2025

12. The current applied to the filament (cathode)in an X-Ray machine is proportional to:

12. The current applied to the filament (cathode)in an X-Ray machine is proportional to:
12. The current applied to the filament (cathode)in an X-Ray machine is proportional to:

Solution
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Answer

Temperature of the filament (cathode). Explanation 1. Identify the relationship The current applied to the filament in an X-Ray machine is proportional to the number of electrons emitted by the cathode. 2. Relate to temperature The emission of electrons from the cathode is governed by thermionic emission, which depends on the temperature of the filament. 3. Apply Richardson's Law According to Richardson's Law, the current density J is given by **J = A T^2 e^{-\frac{W}{kT}}**, where A is a constant, T is the absolute temperature, W is the work function, and k is Boltzmann's constant.

Explanation

1. Identify the relationship<br /> The current applied to the filament in an X-Ray machine is proportional to the number of electrons emitted by the cathode.<br /><br />2. Relate to temperature<br /> The emission of electrons from the cathode is governed by thermionic emission, which depends on the temperature of the filament. <br /><br />3. Apply Richardson's Law<br /> According to Richardson's Law, the current density $J$ is given by **$J = A T^2 e^{-\frac{W}{kT}}$**, where $A$ is a constant, $T$ is the absolute temperature, $W$ is the work function, and $k$ is Boltzmann's constant.
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