A potential difference is applied between the electrodes in...

A potential difference is applied between the electrodes in a gas discharge tube. In $1.0 \mathrm{s}, 3.8 \times 10^{16}$ electrons and $1.2 \times 10^{16}$ singly charged positive ions move in opposite directions through a surface perpendicular to the length of the tube. What is the current in the tube?

Key Concepts

Electric Current

Electric current is the rate at which charge flows through a conductor or space, measured in amperes. It is defined as the total charge passing a given point divided by the time interval during which the charge flows.

Charge Carriers

Charge carriers are particles, such as electrons or ions, that are responsible for carrying electric charge in a medium. In various systems like gas discharges or electrical conductors, these particles move under the influence of an electric field, resulting in an electric current.

Elementary Charge

The elementary charge is the magnitude of the electric charge carried by a single proton or electron. It serves as the fundamental unit for quantifying charge in systems where multiple elementary charges contribute to a total electric current.

Transcript

00:01 Good afternoon, everyone.

00:03 So today we're going to work through a problem where we're asked to determine the current in a given wire where there are this number of electrons passing in a given second in one direction, and the number of protons passing in the other direction.

00:17 Now, the total current is only dependent on the absolute value of the charge.

00:23 So let's go ahead and write that out as an equation.

00:25 Remember, current is a amount of charge that passes a given point in a given amount of time.

00:31 Labeled this as i is equal to the absolute value of the total charge q divided by the change in time.

00:42 Now the problem states that our change in time that these electrons and protons all pass this point in one second, which means we can take this delta t and push it to one.

00:55 All right? so with that being said, we can also rewrite this cue as the number of protons plus the number of electrons multiplied by the elementary charge particle e, which is the charge of an electron, which we have written over here as 1 .6 times 10 to the negative 19th.

01:16 The number of protons that given the problem is 1 .2 times 10 to the 16th, and the number of electrons is 3 .8 times 10 to the 16th.

01:25 Okay, so going back down here, we're ready to solve our problem.

01:29 The total current in the wire is simply going to be equal to i is equal to np which is 1 .2 times 10 to the 16th plus 3 .8 times 10 to the 16th all multiplied by e where e is equal to 1 .6 times 10 to the negative 19.

01:58 Now when we calculate this all out when we add this together and multiply by 1 .6 you're going to get that i is equal to a approximately 0 .008 1 amps...

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