Video Transcript
The following graph shows the
relation between the collector current and the emitter current of transistors. What does the slope of the line
represent? (A) 𝛼 sub 𝑒, (B) 𝛽 sub 𝑒, (C)
one minus 𝛼 sub 𝑒, (D) one plus 𝛽 sub 𝑒.
In order to answer this question,
we must consider the relationships between the components of a transistor circuit:
the emitter, the collector, and the base. In the circuit, the conventional
current directions for each circuit connection to the transistor are as follows. There is a current out of the
emitter region. This can be denoted 𝐼 sub E. There is a current into the
collector region. This can be denoted 𝐼 sub C. There is a current into the base
region. This can be denoted 𝐼 sub B.
In this question, we are most
interested in the relationship between the emitter current and the collector
current. In fact, the graph asks us about
the slope of the line in the graph. The slope of a graph can be
calculated by finding the change in the quantity on the vertical axis, in this case
that’s Δ𝐼 sub C, and dividing it by the change in the quantity on the horizontal
axis. In this case, that’s Δ𝐼 sub E.
Now, it turns out that this
quantity, change in collector current divided by change in emitter current, is an
important quantity in the study of transistors. It is the ratio of how much current
goes into one end of the transistor and how much current leaves the other end. It is also known as the current
gain of the transistor and is denoted with the symbol 𝛼 sub 𝑒.
Looking back at our answer options
then, we see that the quantity representing the slope of the graph we’ve been given
is the current gain 𝛼 sub 𝑒. We choose option (A) as our final
answer.
