Video Transcript
Diagram (a) shows a circuit that
can be used to rectify an alternating current. If the input voltage is that shown
in diagram (b), which of the following graphs shows the output voltage as measured
by the voltmeter in the circuit diagram? [A] Diagram 1 [B] Diagram 2 [C] Diagram 3 [D] Diagram 4
Okay, so in this question, we’ve
got diagram a, which shows the circuit that we’re considering, and diagram b, which
is the input voltage that’s produced by the AC source in this circuit. And as well as this, we’ve been
told that the circuit in diagram a can be used to rectify an alternating
current. Now, based on this information, we
need to work out which one of these four graphs here shows the output voltage as
measured by the voltmeter in the circuit.
Okay, so to answer this question,
let’s first consider what we have in the circuit diagram in diagram a. What we’ve got is an AC source, a
diode, a resistor, and a voltmeter. Now, the AC source, the diode, and
the resistor are in series. And the voltmeter is measuring the
potential difference across the resistor. Now, the AC source is producing a
sinusoidal potential difference across the circuit. And if we had a circuit where there
was no diode, but instead we just had an AC source, the resistor, and the voltmeter,
then the sinusoidally varying potential difference produced by the AC source would
be the same as the potential difference across the resistor. In that situation, we would have a
sinusoidally varying current through the resistor as well.
However, coming back to the circuit
in diagram a, that’s not what we’re going to see because remember we have a
diode. Now, a diode is a circuit component
that only allows current flow through it in one direction. Now, we can choose to say that
anytime the potential difference produced by the AC source is positive, that is
going to generate a current flow in this direction that’s clockwise around the
circuit. And then, we can see that that
current flow is actually allowed to be sustained because current can flow in this
direction through the diode. We can see which direction a diode
allows a current through it by looking at the arrow in that circuit diagram.
And so, anytime the potential
difference is positive produced by the AC source, there is a current in the
clockwise direction in the circuit. Therefore, there is a current
through the resistor in this direction in the circuit. And then for the resistor, we can
recall that the potential difference across the resistor which is the value measured
by the voltmeter is equal to the current through that resistor multiplied by the
resistance of the resistor itself. So the point is that anytime the
potential difference from the source is positive, a current is flowing clockwise
through the circuit which is allowed to flow because of the diode. And so, there is a nonzero current
for the resistor. And if there’s a nonzero current
through the resistor, then the potential difference also is nonzero, where that
potential difference is the voltage measured by the voltmeter. And this is because we’re looking
at Ohm’s law just for the resistor and the resistance of the resistor is a
constant.
Therefore, we can say that the
voltmeter will measure the same potential difference across the resistor as is
produced by the source whenever the source is actually producing a positive
voltage. However, as soon as we look at the
negative portion of the curve, then it’s a whole different story because when the
voltage from the AC source becomes negative, that negative voltage tries to generate
a current in the circuit in the opposite direction to before. In other words, this AC source is
now trying to set up a current in the counterclockwise direction, which would be
fine if it weren’t for the diode because the diode does not allow a current through
it in the opposite direction. And hence, there is no current in
this circuit because there aren’t any other branches for the current to flow through
that don’t end up at the diode at some point.
And so, whenever the potential
difference from the source is negative, there is no current in the circuit. So the current of the resistor is
zero. And then coming back to Ohm’s law
once again, if the current is zero, then the potential difference across the
circuit, which is remember being measured by the voltmeter, is also going to be
zero. So in other words, for the entirety
of the time that the potential difference source is producing a negative voltage,
the voltage measured by the voltmeter itself is going to be zero because there is
zero potential difference across the resistor.
Then, we go back once again to the
positive part of the cycle. And in that situation, once again,
we will have a positive potential difference measured by the voltmeter. And that potential difference will
follow the voltage produced by the AC source. And once again, we return to the
negative part which is going to result in a zero voltage measured by the
voltmeter. And so, all in all, what we expect
to see is something like this when it comes to the potential difference measured by
the voltmeter. And at this point, we can identify
this as a half-wave rectified potential difference.
But more importantly, out of the
four diagrams that we have to choose from, we can see that the first of these
diagrams correctly matches what we’re expecting to see in terms of the voltage
measured by the voltmeter in diagram a.
