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- [Instructor] We are
asked, "How does the current
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"going through R1," so, this resistor,
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"when the switch is open,"
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this switch, "compare to
the current through R1
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"when the switch is closed?"
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Pause this video and see
if you can figure that out.
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Alright, so let's just think
about the two scenarios.
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So, we can view the current as this,
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right over here, this
current that we care about.
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We could either measure it there
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or you could measure it right over there,
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and let's first think about the scenario
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where the switch is open.
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So, our current when our switch is open
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is going to be equal to the voltage
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across the resistors, and
that's going to be our 12 volts,
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12 volts,
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divided by the equivalent
resistance of these resistors.
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When the switch is open, essentially,
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we just have R1 and R2 in series,
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and so this is just gonna be R1+R2.
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If you have two resistors in a series,
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their equivalent resistance is just
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the sum of the resistances.
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Fair enough.
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Now, let's think about the situation
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where the switch is closed.
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Closed.
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So here, our current at
this point of our circuit,
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or the current going through R1,
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so I sub closed,
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is, once again, it's going
to be equal to 12 volts,
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the voltage across the resistors,
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but what are we gonna divide by now?
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When we close the switch, what happens?
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Well, these lines where
we see no resistors
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in circuit diagrams, that's
assumed to be resistance-less,
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so all of the current will
actually flow that way.
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So, by closing this switch,
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you're essentially removing
R2 from the circuit.
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The current will just go through R1,
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and then follow the path of
least resistance, literally.
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And so, in this situation,
our current is going
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to be 12 volt divided
by, you essentially just
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have one resistance, divided by R1.
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So, when you closed the circuit,
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you've essentially taken a resistor out,
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and so if you took a resistor out,
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you're going to increase the current,
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so you could just write it as,
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the current when the switch is open
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is going to be less than,
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is going to be less than the current
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when the switch is closed.
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Once again, why is that?
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Well, just look at the denominators here.
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When the switch is open,
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you're dividing by a larger number
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than when the switch is closed.
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Or, another way of thinking about it,
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when the switch is open, the
R2 resistance is factored in.
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When the switch is closed,
the R2 resistance essentially
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becomes a non-factor and
you have less resistance,
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which would mean you
would have higher current.