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QPage 351: Q3: HC Verma: Concepts of Physics - Volume 2 Electric Current through Gases Page 351: Q3 Solution: How will the thermionic current vary if the filament current is …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often treat the filament current as if the thermionic current rises linearly with it, forgetting that emission follows the Richardson‑Dushman law $J=A T^2 e^{-\phi/kT}$ and that filament temperature (and thus $T$) depends on the heating power $I^2R$. A small increase in filament current can cause a large exponential rise in emitted current, or be limited by space‑charge effects, so always consider the temperature‑exponential relationship rather than a simple proportionality.

How will the thermionic current vary if the filament current is increased?

Step-by-Step Verified Solution

**Answer:** The thermionic current increases. **Step-by-Step Explanation:** Increasing the filament current raises the temperature of the cathode. According to the Richardson-Dushman equation, the rate of thermionic emission increases rapidly with temperature. Hence, more electrons are emitted per unit time, and the thermionic current increases .

All Questions in this Chapter

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