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Circuits
When electric charge flows, we refer to that as the current. For most
modern applications of this, we use wires to contain the electric current.
Other examples of currents are lightning bolts and other movement of
electrically charged particles through space, such as in older TV display
screens, old radio tubes and instruments such as mass spectrometers and
particle colliders.
For this session, we will focus on wired circuits and how to represent them.
Much of the initial discussion will apply equally well to DC circuits (battery
powered or a power source with + and – terminals) or AC circuits (wall
sockets and generators).
First concept: what is an electric circuit?
The diagram at right shows a bulb wired
to a battery, both in drawing form and
as a circuit diagram. The circle used
for a bulb is not a standard symbol, but
it will serve our purposes.
So what about the circuti is important?
Several alternate possibilities for a
circuit are given in the figure at right.
Circle those which would work for
lighting the bulb.
You can experimentally test any of
them you are unsure of using the
batteries and bulbs available.
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What about the other “circuits” made them non-functional?
A ____________________________________________
B ____________________________________________
C ____________________________________________
[this one involves knowing about the bulb’s interior wiring]
D____________________________________________
E ____________________________________________
F_____________________________________________
From these diagnoses, what do you conclude is necessary for a functioning
circuit, in terms of connections between the battery and the components?
If you observed the battery getting hot when you wired any of the circuits,
you probably had what is known as a short circuit or just a short. This is a
circuit where a component doesn’t work because there is a shorter path for
the current to follow with less resistance (hence more current and a hot
battery).
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Equivalent circuits.
One of the basic skills you need to master in this unit is the ability to
determine whether two simple circuit diagrams are equivalent or not.
For these simple diagrams, all connections are made by wire whose
resistance can be neglected (Majicke Physics Shoppe!) . To begin with, we
will deal only with resistors and batteries; the principles will carry over to
other components when we discuss them later.
Consider the following four diagrams with a battery and 3 bulbs.
Which of the four are equivalent?
How many different circuits are there?
Check your answers by using 3 equivalent bulbs and a battery. Do the bulb
brightnesses confirm your answers?
Picture to diagram:
Below are two pictures of circuits and a diagram for the first. Draw a
diagram for the second circuit pictured.
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Now consider the following diagrams and drawings of circuits. Determine
how many different circuits there are and which figures belong to which
group.
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Resistance:
Using resistors and a meter, we can determine how resistances combine. To
keep things simple, we will start with equal resistors.
A resistor looks something like this picture:
The colors of the bands are (Left to Right: brown black orange gold)
This decodes as 103 5% which means R = 10 x 103 Ω. Note the third band is
the multiplier and that this is not scientific notation; no decimal between the
first 2 digits.
The color code:
black brown red
orange yellow green blue
violet gray
white
0
1
2
3
4
5
6
7
8
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Some newer resistors have three digits and a multiplier. There are sites on
the web with the code and the last page of this handout shows the code.
Your resistor color code:____________________________
Resistance value from code: __________ Measured ____________
Now construct the following circuits and measure their resistance.
These arrangements occur often enough that it is convenient to have names
for them. Those on the left are in series and on the right are parallel
combinations.
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If you have trouble remembering series vs. parallel, they can be related to
dance types :
parallel
series
Using your data from the resistor combinations, answer the following:
When resistors are in series, the total resistance is equal to
_________________________________ of the individual resistances.
When resistors are in parallel, the total resistance is given by combining the
individual resistances according to the formula:
Now, suppose you have a resistance of R in parallel with a resistance of 2R.
The total resistance of the combination is then
Verify your answer experimentally.
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Thinking about current.
For the series and parallel combinations below, predict how the current
through each resistor in a given circuit compares. Also predict how the
voltages across the resistors will compare.
Individual currents :
Total current:
Individual voltage:
Individual currents :
Total current:
Individual voltages:
As a demonstration at the front of the room, these circuits will be hooked
up with ammeters. Draw in the ammeters on the circuits above and record
the readings.
You can take your voltmeter and verify your voltage predictions at the same
time. Record these next to the diagrams as well.
Next, construct the following
circuit:
For each resistor, you will
measure the voltage drop
across the resistor (potential
difference) and the current
flowing through it.
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ΔV
I
R1
R2
200Ω
R3
R4
R5
Now let’s see if we can generate some rules based on our measurements.
Consider the current flow. Where can the current go from the top of the
battery as it reaches the branch point?
Looking at your measured currents, can you state a rule about the currents
through each of the resistors on the paths which intersect at the branch
point?
Now consider the voltage drops across the resistors in the upper loop of the
circuit. If you go around the loop and add the voltage drops (with
appropriate sign!), what is the result?
Is this true of the voltage drops around the other possible loops in the
circuit?
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A new tool: the Volt-Ohm Milliammeter or VOM or Voltmeter
For the rest of the term, and on into next, we will be using the VOM to make
a variety of measurements. This is also a handy tool around the car, house
and any lab where electrical measurements are made. The basic device can
be used to measure voltage, resistance or current, but you need to know how
to use it in each mode.
First, a look at a typical VOM :
DC volts scales
Start high and
lower to get
more digits.
AC volts, AC
will read 0 on
DC scale
Resistance in Ω
(Ohms)
Amps (current)
Start high and
work down to
protect meter.
There is a 2nd
jack for high
current.
Common (-) jack
Cautions:
(1) always turn the meter off when not in use, to save batteries and possible
damage to meter if connected accidentally.
(2) If measuring current, make sure you start at a high enough range or you
will burn out the fuse in the meter. The meter is also connected differently
to measure current, so pay attention when you do so.
Units: For now, all you need to know is that a potential of one Volt across a
resistance of one Ohm drives a current of one Amp or
1V = (1A) (1Ω),
Ohm’s Law: V = IR
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Connecting the voltmeter:
Connect the black lead to the common jack.
Potential (Voltage): Connect red lead to the VΩmA jack. Touch the leads
to the two points you wish to measure the potential difference between,
leaving the other circuit connections in place.
Resistance (Ohms): Connect red lead to the VΩmA
jack. Touch the leads to the two points you wish to
measure the resistance between. Be aware that this
will measure the equivalent resistance of everything
connected between the two points, so you may wish to
disconnect some parts of a circuit to get the
resistance of a specific portion.
Current (Amps): For lower currents, connect red lead to the VΩmA jack.
If you aren’t sure what to expect, connect to the 10A jack instead.
To measure current, the meter is put in
series with the circuit; think of this as
replacing a wire with the meter. This is
different from the above connections.
(picture from a very useful site:
www.allaboutcircuits.com/ ; a great site with
lots of worksheets and lessons on circuits.)
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http://www.emsb.qc.ca/laurenhill/science/resistor.jpg, Lauren Hill Academy in Quebec.
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