Electric Conduction in Gases

An electrical network is a combination of electrical components like resistors, inductors, capacitors, power sources, and switches. It can be analyzed using various laws and theorems such as Ohm's Law, Kirchhoff's Laws, Thevenin's and Norton's theorems. Below are detailed analyses of such networks using theoretical tools and mathematical modeling.

Electric Conduction in Gases

Electric conduction in gases occurs due to ionization, where neutral gas molecules are converted into ions and free electrons. This process allows the gas to conduct electric current under specific conditions.

Ionization and Breakdown Potential

Gases under normal conditions are non-conductors due to their neutral molecular composition. However, when subjected to high voltage (breakdown potential), ionization occurs:

$Breakdown\ Potential = V_{min}$

This is the minimum voltage required to initiate conduction. Once ionized, an electric field causes electrons and positive ions to move in opposite directions, forming a current.

Mechanism of Discharge in Gases

At reduced pressure and high voltage, different stages of electric discharge occur in a partially evacuated tube as shown in Figure 1.23 and Figure 1.24:

1. Violet streamers pass between cathode and anode.
2. A pink positive column and negative glow near the cathode.
3. The positive column becomes striated; the negative glow moves away from the cathode.
4. Crookes' dark space fills the tube.

Effect of Pressure on Discharge

As pressure decreases:

• At ~20 mmHg: Brush discharge at electrodes; violet streamers appear (Figure 1.24a).
• Further reduction leads to salmon pink glow that fills the tube.
• At ~5 mmHg: A dark space forms near the cathode, developing into Crookes' dark space.

Applications of Gas Conduction

Electric conduction in gases is applied in:

• Sodium vapor and mercury lamps
• Fluorescent lights
• Neon signs
• Arc welding
• Cathode ray tubes (CRTs)

Optical Emission

Ionized gases emit characteristic spectral lines due to electrons transitioning between energy levels, which can be analyzed using spectroscopy.

Mathematical Model for Ionization Current

The current in a gas discharge can be modeled using Townsend's first ionization coefficient $alpha$:

$I = I_0 e^{\alpha d}$

• $I_0$: Initial current
• $alpha$: Ionization per unit length
• $d$: Distance between electrodes

As the voltage increases, the ionization becomes self-sustaining, leading to a glow or arc discharge depending on pressure and gas type.