The essential condition for the Paschen’s law to be valid is that
(A) voltage must be dc
(B) voltage must be ac
(C) temperature must be constant
(D) humidity must be low.
The Correct Answer and Explanation is:
Correct Answer: (A) Voltage must be DC
Explanation (300+ Words):
Paschen’s Law describes the breakdown voltage (minimum voltage required to cause an electrical discharge or spark) between two electrodes in a gas as a function of the product of the gas pressure (p) and the distance (d) between the electrodes. The law is mathematically given as: V=B⋅pdln(A⋅pd)−ln[ln(1+1γ)]V = \frac{B \cdot pd}{\ln (A \cdot pd) – \ln [\ln (1 + \frac{1}{\gamma})]}
Where:
- VV = breakdown voltage
- pp = pressure of the gas
- dd = distance between the electrodes
- AA and BB = constants depending on the type of gas
- γ\gamma = secondary ionization coefficient (depends on the material of electrodes and gas)
Why Option (A) is Correct:
Paschen’s law applies under the condition that the voltage applied is direct current (DC). This is essential because:
- Stable Electric Field: DC voltage provides a constant electric field, which allows the ionization process to build up steadily in the gas. Electrons gain energy continuously in one direction, which helps in initiating and sustaining an avalanche breakdown process.
- Predictable Breakdown: Since the field is not changing direction as in AC, the behavior of gas breakdown becomes predictable, allowing accurate application of Paschen’s law.
Why Other Options Are Incorrect:
- (B) Voltage must be AC:
AC voltage alternates direction, and the electric field reverses periodically. This makes it harder to accumulate the steady ionization required for Paschen’s law to hold. It also introduces complexities like capacitive effects and displacement currents that are not part of Paschen’s assumptions. - (C) Temperature must be constant:
While temperature can influence gas behavior (e.g., pressure), it is not a strict requirement for the validity of Paschen’s law. Moderate temperature changes are usually acceptable within the practical range of the law. - (D) Humidity must be low:
High humidity can affect the dielectric strength of air, but Paschen’s law still applies to moist air—though with altered constants. Thus, low humidity is not an essential condition.
Conclusion:
The essential condition for the valid application of Paschen’s Law is that the applied voltage must be DC, making option (A) the correct answer.