### Video Transcript

The following circuit diagram shows a transistor used as a switch. By inspecting the diagram, determine whether the switch is off or on and find the
current division, ๐ผ ๐. (A) The switch is on and the current division is 0.96. (B) The switch is on and the current division is 0.04. (C) The switch is off and the current division is 0.96. Or (D) the switch is off and the current division is 0.04.

This is the circuit symbol for the transistor. It helps us discern certain properties of the transistor thanks to this little
arrow. Because the arrow is pointing outward, we know that this is an NPN transistor rather
than a PNP transistor, which has an arrow pointing inward. We can also recall that in any transistor symbol, the arrowhead is always drawn so
that itโs connected to the emitter region. That means that in our diagram, the emitter is here. We can then tell that the collector must be here and the base is in between the
emitter and the collector.

So, now that weโve labeled the transistor, letโs also notice these current values
labeled on the diagram. We can tell that 72 milliamps is the collector current, so weโll label this ๐ผ C. And the three-milliamp current must be the base current, so weโll label it ๐ผ B. We can see that the base current here is much smaller than the collector current. This is what weโd usually expect from a transistor.

Recall that a transistor can act as a switch. The existence of a base current enables a collector current to flow. In this case, weโd say the transistor was on. But if thereโs no base current, the collector current canโt flow, so the transistor
is off. Because there is a base current here, we can say that the switch formed by this
transistor is effectively on. Now, options (C) and (D) both say that the switch is off, so we can rule these
options out.

Now, we also need to find the current division, which is represented by ๐ผ ๐. We can do this using the formula ๐ผ C equals ๐ผ E times ๐ผ ๐, where ๐ผ C is the
collector current, ๐ผ E is the emitter current, and ๐ผ ๐ is the current
division. This equation effectively defines the current division as being the constant of
proportionality between the collector current and the emitter current.

We can make the current division the subject of this equation by dividing both sides
by ๐ผ E. This gives us ๐ผ C over ๐ผ E equals ๐ผ ๐. And we can swap the left- and right-hand sides of this expression around to give us
๐ผ ๐ equals ๐ผ C over ๐ผ E. So we could also think of the current division as being the ratio between the
collector current and the base current.

Now, weโve been given ๐ผ C, but we donโt yet know ๐ผ E. Fortunately, this is easy to calculate. We just need to remember that the emitter current, thatโs here on our diagram, is
equal to the sum of the collector current and the base current. Written as an equation, we have ๐ผ E equals ๐ผ C plus ๐ผ B.

Now, using the values for ๐ผ C and ๐ผ B given in the diagram, we can calculate that
the emitter current is 75 milliamps. Weโre now ready to solve for the current division. The collector current is 72 milliamps, and the emitter current is 75 milliamps. Typing this into a calculator, we find that the current division is equal to
0.96.

Note that this is a dimensionless number since the units of current cancel each other
out in the numerator and denominator. This means the correct answer to the question is option (A). The switch is on and the current division is 0.96.