Video Transcript
An NPN transistor is connected to a
power supply with voltage 𝑉 CC. A power supply with voltage 𝑉 EB
is connected across the transistor’s emitter and base terminals, as shown in the
diagram. There is a current 𝐼 C between 𝑉
CC and the collector terminal, a current 𝐼 E between 𝑉 EB and the emitter
terminal, and a current 𝐼 B between 𝑉 EB and the base terminal. An external resistance 𝑅 C is
placed between 𝑉 CC and the collector terminal. And an external resistance 𝑅 B is
placed between 𝑉 EB and the base terminal. The potential difference across the
collector and emitter terminals is 𝑉 CE. If the value of 𝑅 B is reduced,
which of the following most correctly describes the effect on the value of 𝐼 C? 𝐼 C increases, 𝐼 C decreases, 𝐼
C is constant.
All of the information in the upper
paragraph is contained in the diagram. So we can clear away the upper
paragraph to make some space to work. Alright, so the question asked us
to relate 𝑅 B to 𝐼 C. Looking at the diagram, we see that
𝑅 B is the resistance in one branch of the circuit and 𝐼 C is the current in a
different branch of the circuit. So it’s not immediately obvious how
the resistance in one branch is related to the current in the other branch.
Since it’s not obvious how these
two are directly related, let’s see if there is a third intermediate quantity. If we can relate 𝑅 B to this third
quantity and this third quantity to 𝐼 C, then we should be able to relate 𝑅 B to
𝐼 C. Looking back at the diagram, 𝐼 B,
the current in the same branch of the circuit as 𝑅 B, looks like something we
should be able to relate to 𝑅 B. In fact, they are related. We recall that Ohm’s law for direct
current circuits tells us that the voltage is equal to the current times the
resistance in the circuit. What Ohm’s law tells us is that in
a purely resistive circuit with a constant voltage, current and resistance are
inversely proportional.
Now the voltage 𝑉 EB is
constant. But it’s not true that the circuit
is purely resistive because we have effects from the transistor that we haven’t
fully characterized. Nevertheless, the qualitative
statement of Ohm’s law remains true. Although 𝐼 B and 𝑅 B will not
necessarily be truly inversely proportional, as 𝑅 B decreases, 𝐼 B should increase
and vice versa. It is important to stress that this
statement is only qualitatively true. We cannot use Ohm’s law to make
quantitative statements without further understanding the behavior of the
transistor. Nevertheless, the question only
asks us for a qualitative relationship. So a qualitative statement is all
that we need.
Now remember, our goal is to relate
𝑅 B to 𝐼 C. So now that we’ve related 𝑅 B to
𝐼 B, we need to relate 𝐼 B to 𝐼 C. To do this, we note that 𝐼 B is
the base current of the transistor. And we recall that transistors can
act as amplifiers. When transistors act as amplifiers,
the small base current acts as an input signal that modulates or controls the
collector current and ultimately the current that exits the transistor. One of the important properties of
an amplifier is that the signal maintains its shape. That is, the output signal must be
directly proportional to the input signal.
Now, if 𝐼 E, the output current,
is directly proportional to 𝐼 B, the input current, then it must be the case that
𝐼 C is also directly proportional to 𝐼 B. This must be true because 𝐼 E is a
multiple of 𝐼 B. And 𝐼 E is also 𝐼 B plus 𝐼
C. So if 𝐼 B plus 𝐼 C is a multiple
of 𝐼 B, then 𝐼 C must also be a multiple of 𝐼 B. In fact, the constant of
proportionality between 𝐼 C and 𝐼 B has a special name. It is called the dc current
gain. And there we have it. We have related 𝐼 C to 𝐼 B and
also 𝑅 B to 𝐼 B. And by combining these two
relationships, we can relate 𝑅 B to 𝐼 C.
The question is asking us what
happens when 𝑅 B is reduced. Given our relationships, when 𝑅 B
is reduced, 𝐼 B increases. And when 𝐼 B increases, 𝐼 C,
which is directly proportional to 𝐼 B, must also increase. And that’s our answer. As 𝑅 B is reduced, 𝐼 C
increases.
Alright, let’s move on to the
second part of the question.
If the value of 𝑅 B is increased,
which of the following most correctly describes the effect on the value of 𝐼 C? 𝐼 C increases; 𝐼 C decreases; 𝐼
C is constant.
This is very similar to the
question that we just answered. And in fact, we have already worked
out all of the information that we need to answer this question as well. If 𝐼 B increases as 𝑅 B
decreases, then as 𝑅 B increases, 𝐼 B decreases. And as 𝐼 B decreases, 𝐼 C, being
proportional to 𝐼 B, decreases as well. So as the value of 𝑅 B is
increased, 𝐼 C must decrease. And there’s our answer. As 𝑅 B is reduced, 𝐼 C
increases. And as 𝑅 B has increased, 𝐼 C
decreases.
