What is the role of resistors in a vacuum tube circuit?

[TobeHode]

Homework Statement

Hello. I am having trouble understanding the simple circuit diagram that is attached.
I need to explain what the function of the two resistors are. I know some basic things about circuits (Ohms law, Kirchoffs loop rules,etc.) but I do not know exactly how a vacuum tube functions in a circuit.

Hint: Consider the energy of the electrons leaving each end of the filament.

Sorry about the diagram, I made it in paint. The line connecting the resistors to ground does not connect to either line going to filament power. I tried to indicate this.

Homework Equations

The Attempt at a Solution

So here is what I do know. There is a tungsten filament (the cathode) that heats up and when the temperature gets hot enough, electrons are emitted (thermionic emission) creating a space charge around the filament. By applying a positive potential to the anode, the flow of electrons will go from cathode to anode resulting in a current.

The purpose of this circuit was to show the characteristics of thermionic emission. Various values of filament current (the A ammeter) and filament voltage was used to record the anode current (the mA ammeter) for a range of anode voltage.

The potential is different at each end of the filament. In regard to the hint, this make me think that the resistors somehow negate the effect of having different potentials at each end of the filament. How this happens, I do not understand.

I am not looking for a flat out answer, rather some insight into how this circuit functions. I think If I can get an idea of how exactly the current flows then I should be able to answer the original question.

 

[Sciurus]

The purpose of this circuit was to show the characteristics of thermionic emission. Various values of filament current (the A ammeter) and filament voltage was used to record the anode current (the mA ammeter) for a range of anode voltage.

The potential is different at each end of the filament. In regard to the hint, this make me think that the resistors somehow negate the effect of having different potentials at each end of the filament. How this happens, I do not understand.

I might be wrong on this, but it seems like you could consider that the filament acts like a resistor itself. The center tap of a voltage divider would be the same potential as the center of the filament, I think.

 

[TobeHode]

Thanks for responding. I do believe the filament acts like a resistor. I do not understand why you say that the center tap of a voltage divider would be the same potential as the center of the filament. Could you explain a bit more?

 

[Sciurus]

Well, you could make a resistor out of a long piece of wire -- all wire has some small resistance. And when you run current through a wire, it heats. So the filament is probably very similar.

The voltage at different points of the wire vary gradually from the voltage at one end of the wire to the other (assuming the wire is uniform).

 

[TobeHode]

Well, you could make a resistor out of a long piece of wire -- all wire has some small resistance. And when you run current through a wire, it heats. So the filament is probably very similar.

The voltage at different points of the wire vary gradually from the voltage at one end of the wire to the other (assuming the wire is uniform).

Yes, I understand how the filament is acting like a resistor.

I do not understand why you say that the potential in between the 100 ohm resistors is the same as the potential at the filament center.

Can you explain why you say the resistors have that effect?

 

[Sciurus]

I'm working on the assumption that the filament is symmetric, and therefore could be modeled as

-- RESISTOR -- CENTER -- RESISTOR --

Since the heating wire acts as a resistor and is the same on both sides of the center point of the filament, both "resistors" have the same value.

 

[TobeHode]

Thanks again for replying.

Hmm, I am still having trouble understanding. It seems to me that the potential at the center of the filament is dependent on the resistance of the filament. It seems as though the filament being modeled as resistor-center-resistor requires each "resistor" to be 100 ohms in order to match the potential at the center of the actual 2 100 ohm resistors.

Am I forgetting something basic here?

 

[Sciurus]

I'm just going to use a schematic from the web to avoid drawing one.

Since each series pair of resistors is an independent path, the voltage at the center depends on the resistance of the resistors above and below. If the left two are 500 ohms each, both will have the same magnitude voltage across them. If VE is 10 V, each will have 5 V from one lead to the other.

On the right, the resistance could be say, 100 ohms, and again each would have 5 V difference between the leads if VE = 10 V, and if we say that the bottom of the schematic is grounded, the center point would read +5 volts relative to ground, half the supply voltage of +10 V.

 

[TobeHode]

Since each series pair of resistors is an independent path, the voltage at the center depends on the resistance of the resistors above and below. If the left two are 500 ohms each, both will have the same magnitude voltage across them. If VE is 10 V, each will have 5 V from one lead to the other.

On the right, the resistance could be say, 100 ohms, and again each would have 5 V difference between the leads if VE = 10 V, and if we say that the bottom of the schematic is grounded, the center point would read +5 volts relative to ground, half the supply voltage of +10 V.

I agree with your description.

So, then would you say that in the original circuit, the voltage of one of the leads of the volt-meter closest to the anode power is at the same voltage as the center of the filament?

If so, then that seems to imply that the resistors maintain the filament voltage at 0 relative to the applied anode voltage provided that the applied voltage is greater than the filament voltage.

 

[Sciurus]

I agree with your description.

So, then would you say that in the original circuit, the voltage of one of the leads of the volt-meter closest to the anode power is at the same voltage as the center of the filament?

If so, then that seems to imply that the resistors maintain the filament voltage at 0 relative to the applied anode voltage provided that the applied voltage is greater than the filament voltage.

Yup, sounds good. The filament center will always be zero volts since the center of the 100 ohm resistors is grounded. It make it a nice little test circuit.