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It's hard to imagine what life would be like
without our ability to harness electricity
to light our buildings and run our endless array
of electrical powered devices.
In another segment,
we saw what a simple circuit
called a series circuit looks like.
We saw that the more bulbs you add,
the dimmer the bulbs
because the voltage is being shared across them,
and if one went out, they all did.
So, how did we get to this?
So many lights all delivering equal amounts of voltage,
and when one goes out, we simply replace it,
while the others continue to shine.
The answer is an ingenious kind of circuit
called a parallel circuit.
It's a simple, logical solution
to provide the basic wiring we need
to supply electricity to our communities.
A parallel circuit is...
Each resistor connected in a separate path
receives the full circuit voltage.
The total circuit current is equal to the sum
of the individual branch currents.
Let's build a parallel circuit,
so we can see just how it works.
I've got everything we need here
to create a parallel circuit--
bulbs, wires, and power supply,
these batteries.
Let's hook this up,
and then we'll analyze what's going on.
I'll just connect this wire right here.
And, of course, the bulbs light up.
Let's look more closely at what makes it
a parallel circuit.
See those wires running in parallel?
The Rs with the zig zags are resistors,
an electrical component that limits or regulates
the flow of electrical current in a circuit.
In our case, it's the filaments in the bulbs.
When the current moves through them,
higher resistance in the filament wires
makes them glow.
In a parallel circuit,
the current can flow down
any of the branches and then recombine.
The other thing to remember about parallel circuits
is that the current is not necessarily
the same throughout.
The different branches can have different amounts of resistance
depending on how many resistors you have in the branch.
Those with less resistance draw more current,
and those with more draw less.
That's because, logically enough,
if there is less resistance to the flow of the charge,
more charge will flow.
And if there is more resistance,
what happens?
Less charge can get through in a given amount of time.
You might remember that the voltage across a circuit
can also be explained as the difference in potential
from one end of the circuit to the other.
No matter how many branches you add,
the voltage will be the same across each.
In a parallel circuit,
a charge doesn't pass through
every resistor.
Instead, it passes along a single branch
and then back to the battery.
It doesn't matter whether the charge passes through
resistor one, resistor two,
or resistor three.
The voltage drop across the resistor
in a single branch
must equal the voltage of the battery.
So, each bulb experiences the full potential difference,
V, supplied by the battery.
This is very important
because it means that we can add bulbs
to the circuit and have them all light up
with the same brightness as if there was only one bulb.
In fact, no matter how many bulbs we add,
as long as we have the same resistance
and added one per parallel branch,
they will be as bright as the original bulb.
Do the bulbs look like they have the same brightness?
They do, don't they?
And that characteristic of electricity and circuitry
lets us light up our world.
But how does the voltage stay the same
when there are more bulbs?
If we call the potential difference
created by the battery V,
then all branches of the circuit
must expend V volts.
So, each bulb experiences the full potential difference, V,
supplied by the battery.
When we're working with a parallel circuit,
we can add up resistors to find the total
or equivalent resistance of a circuit.
Let's start with the simple case of two resistors,
each six ohms
on different parallel branches.
Since the circuit offers two equal pathways
for charge to flow through,
only one-half of the charge will pass through
a given branch.
While each individual branch offers six ohms of resistance
to any charge that flows through it,
only one-half of all the charge
will encounter the six-ohm resistance.
The presence of two six ohms resistors in parallel
would be equivalent to having one three-ohm resistor
in the circuit.
When working with parallel circuits,
we can add resistors like this.
One over the equivalent circuit resistance
equals one over the first resistor's resistance
plus one over the second resistor's resistance,
and so on, up through the last resistor.
So, for this circuit,
one over the total resistance
equals one over six ohms
plus one over six ohms.
That totals three ohms,
and that's the total equivalent resistance
of all the resistors in the circuit.
So, remember, the total resistance
is less than any of the individual resistor values.
That's always true in parallel circuits.
Now that we know the total circuit resistance,
we can figure out the overall circuit current
using Ohm's Law.
Parallel circuits are great for things like car headlights
so that if one burns out,
the other still shines,
or a lamp with several bulbs.
If one burns out, the others stay lit.
In fact,
a lot of household wiring is parallel.
Otherwise, if you turned your television
or any other electrical device off,
the rest of the electrical stuff in your home
wouldn't work either.
Why? Because you broke the circuit.
Good thing we have parallel circuits, right?
Now, let's talk about another kind of circuit,
the complex circuit,
which is a combination of series
and parallel circuits.
In a series circuit,
which we explained in another segment,
the wiring simply goes in a loop.
In parallel circuits,
the wiring branches and splits.
In a complex circuit, we have both.
But, how do we figure out what we need?
This is called a VIR chart,
and it shows you how voltage,
current, and resistors
behave in circuits.
We can use the chart to figure out
how much current runs through
a given resistor,
the voltage across that resistor,
or the equivalent resistance
or current for the entire circuit.
The V is voltage,
I is for current,
and R is resistance.
Ohm's law tells us that voltage
is equal to current times resistance.
For a given row,
that represents the value
for a given resistor.
So, if we know two
out of three variables,
we can find the third.
Let's figure out a sample complex circuit.
This is a general example.
Let's find the current through
and voltage across each resistor.
We have our speakers,
a video monitor, a video player,
and a gaming system in this diagram.
Let's fill in what we know.
We can put all of our resistors' values
in the right-hand column.
We know that our power source
is 110 volts,
so we can fill that in
for the total voltage of the circuit
at the bottom of the second column.
Often, our first step in solving complex circuits
is to find overall circuit resistance
and then overall current.
We do this by adding circuit resistors together
until we are left with a single equivalent resistance
for the whole circuit.
Remember that when you add resistors,
you must be aware of whether you are adding
in series or parallel
since different addition rules apply to each.
As we go, we'll see updated circuit diagrams
that reflect the resistors we've combined.
There are lots of approaches we can take
to solve these problems.
Let's begin where resistors are in parallel in a circuit.
One over our equivalent resistance
for our resistors in parallel
equals one over our first resistor in parallel,
two ohms, plus one
over our second resistor in parallel,
fifteen ohms, plus one
over our third resistor in parallel,
twelve ohms.
When we add the three resistors
in the video branches,
we get an equivalent resistance
of 1.5 ohms.
Now, all we need to do,
is add these three resistors together
in series.
That will give us our total equivalent resistance
for this circuit.
Since the resistors are in series,
we add them using our series addition rule
and find that the total resistance
in this circuit is 9.5 ohms.
Now, here is our complex circuit
simplified to a single equivalent resistance.
Now that we know the equivalent resistance of the circuit,
we can put that value into our VIR chart.
Since we know two out of the three variables,
we can use Ohm's law to solve
for the total current in the circuit.
We can rearrange Ohm's law
to solve for current.
Current is equal to voltage
divided by resistance.
When we plug those values in,
we find the total circuit current
is 11.6 amps.
Now, let's go back to our VIR chart
and fill in what we've found,
which is total current.
We can choose among several options
to fill in the rest of the blanks.
We just choose one and go with it.
Let's figure out the current
in each of the five circuit resistors.
We'll use the fact that in a parallel circuit,
the total current equals the sum
of all of the currents
through the resistors,
and, in a series circuit,
total current is the same for all of the resistors
in a circuit.
Right away, we know the current
running through the two four-ohm resistors
that are in series is 11.6 amps.
So, we put 11.6 amps as our current
for those resistors in our chart.
We now have two out of three variables,
so we can find the voltage
across each of those resistors.
Using Ohm's law,
we can find the voltage drop
across each four-ohm resistor.
Voltage equals 11.6 amps
times 4 ohms,
so it comes out to 46.4 volts
per 4-ohm resistor.
Now, we'll put those values into our chart.
Now, let's look at the relationship
between the voltage in series
and parallel circuits,
which is similar to that of current,
but it's flipped like this.
The total voltage in a series circuit
equals the sum of all of the voltages
through the resistors.
In a parallel circuit,
total voltage is the same
for all resistors in parallel.
Since each four-ohm resistor
has a voltage across them of 46.4 volts,
this gives us a total voltage drop
across those resistors and series
of 92.8 volts.
That means the total voltage drop
over the entire parallel circuit branch
is 110 volts,
the total voltage of the circuit
minus 92.8 volts,
the voltage drop across the two resistors
in series, which gives us 17.2 volts.
For the resistors in parallel,
each one must use up the same voltage,
17.2 volts.
We can now plug that value into our chart
for the voltage across the two-ohm,
fifteen ohm,
and twelve-ohm resistors.
We now know two out of three variables
in these rows,
so we can solve for current,
again using Ohm's law.
Let's rearrange the Ohm's law equation, again.
So, current is equal to the voltage
divided by resistance,
and we find the current for our two-ohm resistor
is 17.2 volts
divided by 2 ohms,
which is 8.6 amps.
For the 15-ohm resistor,
it's 17.2 volts divided by 15 ohms,
which is 1.2 amps.
For the 12-ohm resistor,
it's 17.2 volts
divided by 12 ohms or 1.4 amps.
In this segment,
we've looked at parallel and complex circuits,
which we use for all kinds of applications in daily life.
We also saw how to calculate current, resistance,
and voltage, which we use to construct circuits
that are safe and do what we need them to do.
For more practice with circuit equations,
check out the Closer Look.
That's it for this segment of "Physics in Motion."
We'll see you next time.
(announcer) For more practice problems,
lab activities, and note-taking guides,
check out the "Physics in Motion" toolkit.