Question Video: Understanding the Relation between the Collector Current and the External Resistance of an NPN Transistor | Nagwa Question Video: Understanding the Relation between the Collector Current and the External Resistance of an NPN Transistor | Nagwa

# Question Video: Understanding the Relation between the Collector Current and the External Resistance of an NPN Transistor Physics • Third Year of Secondary School

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An NPN transistor is connected to a power supply with a voltage π_CC. A power supply with a voltage π_BE is connected across the transistorβs emitter and base terminals, as shown in the diagram. There is a current πΌ_C between π_CC and the collector terminal, a current πΌ_E between π_BE and the emitter terminal, and a current πΌ_B between π_BE and the base terminal. An external resistance π_C is placed between π_CC and the collector terminal. And an external resistance π_B is placed between π_BE and the base terminal. The potential difference across the collector and emitter terminals is π_CE. The value of π_B is varied. Which colored line on the graph shown most correctly represents the variation in πΌ_C with π_B?

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### Video Transcript

An NPN transistor is connected to a power supply with a voltage π CC. A power supply with a voltage π BE is connected across the transistorβs emitter and base terminals, as shown in the diagram. There is a current πΌ C between π CC and the collector terminal, a current πΌ E between π BE and the emitter terminal, and a current πΌ B between π BE and the base terminal. An external resistance π C is placed between π CC and the collector terminal. And an external resistance π B is placed between π BE and the base terminal. The potential difference across the collector and emitter terminals is π CE. The value of π B is varied. Which colored line on the graph shown most correctly represents the variation in πΌ C with π B?

This question is essentially asking us to find the relationship between the current into the collector, πΌ C, and the resistance of the resistor along the path to the base, π B. If we can find this relationship, then we should be able to determine which line on the graph is the correct one. Letβs begin by recalling the equation for current gain, which can help us relate πΌ C and πΌ B. The current gain of a transistor, π½ sub π, is equal to the collector current divided by the base current.

This equation looks fine, but weβre being asked to compare πΌ C, a current, with π B, a resistance. If we use Ohmβs law for the components for the base of the transistor, then we will have that the potential difference of the power supply π BE is equal to the product of πΌ B and π B. Since π BE is a constant power supply, the potential difference wonβt change. This means that an increase in π B will have to result in a decrease of πΌ B so that the total potential difference remains the same.

If we then look at the equation for the current gain, weβll see that a decrease in πΌ B must also result in a decrease in πΌ C if the current gain remains constant as well. Therefore, an increase in π B, and subsequently a decrease in πΌ B, will result in a decrease in πΌ C.

Looking back at the graph, we see that all five lines are showing some form of decrease, so now we just have to determine which one is correct. We may be tempted to choose the red line, since the relationship seems obvious. If we cut πΌ B in half, then we should expect πΌ C to similarly get cut in half in order to maintain the same current gain. This would mean that there should be a more-or-less linear relationship, which is what the red line shows.

However, this is not actually the case because the current gain is not always constant. Specifically, there are two different scenarios in which current gain is more or less constant: when a transistor is acting as a closed switch and when it is acting as an open switch. Otherwise, current gain changes depending on the values of πΌ B and πΌ C.

To see why this is, letβs recall that a transistor is made up of three semiconductors, labeled differently as the collector, the base, and the emitter. In order for there to be a current across the transistor, all three parts of it must allow conduction. However, the base will not allow any charge through it by itself. Current must be driven into the base in order for the baseβcollector boundary to become forward biased, which will allow a current to be conducted through the transistor. This means that the transistor cannot have a current and thus no collector current πΌ C when there is no current through the base independently, πΌ B.

The current gain at these very small values of πΌ B is quite high, meaning even small increases in πΌ B will result in large increases in πΌ C. We see this represented by the blue, black, and pink lines in the graph here. They have sharp curves that indicate a high current gain at the region to the right. Remember that a high base resistance π B indicates a low base current πΌ B. So since only these three lines indicate a proper change in current gain, the red and green lines must not be correct.

Continuing to look at these three lines, we see that as πΌ B increases, which is to say as π B decreases, the collector current πΌ C levels off. This is because the current gain becomes lower as πΌ B increases.

But which colored line is correct? Letβs look at each individually. The blue line shows a very steep current gain at high π B levels that levels off as π B decreases. The collector current value gradually increases beyond the initial sharp increase but never hits a particular limit. This line then does not accurately portray what happens to the collector current because it actually does hit a current limit.

In transistors, there is a limit to the output current, called the saturation current, for high values of input current. For this transistor setup, the output current is the collector current. The input current is the base current, meaning that we should see a current limit in this graph here. However, for the blue line, it is always gradually increasing as the base current increases, which is not the actual behavior of transistors.

So the blue line canβt be it, nor can the pink line be correct, as we see that the line is very straight, with a distinct break where the current gain apparently changes. These straight lines arenβt representative of the behavior we would expect of a transistor, which involves sharp yet granular changes in current gain. So the pink line isnβt correct either.

This means the only line that can be correct is the black line, which we see correctly shows a large current gain at high values of π B and reaches a limit in the current gained, the saturation current, as π B decreases. The saturation current and sharp changes in current gain for transistors is desirable for their use in electronics. A small change in πΌ B can cause a much greater change in πΌ C, allowing a circuit with a transistor to effectively switch πΌ C on or off, either having no current or reaching a specific saturation current. This means that the colored line on the graph that most accurately represents the variation in πΌ C with π B is the black line.

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