Current in Hydrogen Gas Discharge Tube

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Electric Circuits Beginner Electric Current

Source: High school physics (Chinese)

Problem

In a gas discharge tube, when the voltage between the two electrodes is sufficiently high, a large number of gas molecules are ionized into electrons and positive ions, making the gas conductive. In a hydrogen gas discharge tube, $3.1 \times 10^{18}$ electrons and $1.1 \times 10^{18}$ hydrogen ions pass through a certain cross-section of the tube per second.

Find the magnitude and direction of the current in the tube.
$I \approx 0.67$ A, directed along the motion of the positive ions (anode to cathode inside the tube).

Electrons and positive ions move in opposite directions, but their contributions to the conventional current add together (negative charges moving one way is equivalent to positive charges moving the other way).

The total charge crossing the section per second is:

$$I = (N_e + N_+) e$$

where $e = 1.6 \times 10^{-19}$ C is the elementary charge.

Substituting:

$$I = (3.1 \times 10^{18} + 1.1 \times 10^{18}) \times 1.6 \times 10^{-19} \text{ A}$$ $$I = 4.2 \times 10^{18} \times 1.6 \times 10^{-19} \text{ A} \approx 0.67 \text{ A}$$

The direction of the conventional current is the direction in which the positive hydrogen ions move (from the anode to the cathode inside the tube).