# Introducing

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```					Introducing
Current
And
Direct Current Circuits
Current
Current is defined as the flow of
positive charge.
I = Q/t
   I: current in Amperes or Amps (A)
   Q: charge in Coulombs (C)
   t: time in seconds
Charge carriers
In a normal electrical circuit, it is the
electrons that carry the charge.
e-
So if the electrons move this way,
which way does the current move?

I
Sample problem
How many electrons per hour flow past a point in a
circuit if it bears 11.4 mA of direct current?

If the electrons are moving north, in which direction is
the current?
Cell
Cells convert chemical energy into electrical
energy.
The potential difference (voltage) provided by
a cell is called its electromotive force (or
emf).
The emf of a cell is constant, until near the
end of the cell’s useful lifetime.
The emf is not really a force. It’s one of the
biggest misnomers in physics!
Battery
A battery is composed of more than one
cell in series.
The emf of a battery is the sum of the
emf’s of the cells.
Circuit components

Cell

Battery
Sample problem
If a typical AA cell has an emf of 1.5 V, how much emf
do 4 AA cells provide?
Draw the battery composed of these 4 cells.
Circuit components

Light bulb

Wire

Switch
Circuit components

V     Voltmeter

W     Ohmmeter

A     Ammeter
Sample problem
Draw a single loop circuit that contains a
cell, a light bulb, and a switch. Name the
components

bulb

cell

switch
Sample problem
Now put a voltmeter in the circuit so it reads
the potential difference across the light
bulb.
V

bulb

cell

switch
Series arrangement of
components

Series components are put together so
that all the current must go through
each one

I

Three bulbs in series all have
the same current.
Parallel arrangement of
components

Parallel components are put together so
that the current divides, and each
component gets only a fraction of it.
1/3 I
1/3 I
I            1/3 I                I
1/3 I

1/3 I Three bulbs in parallel

1/3 I
Sample problem
Draw a circuit with a cell and two bulbs in
series.
Sample problem
Draw a circuit having a cell and four bulbs.
Exactly two of the bulbs must be in parallel.
Minilab #1
Draw a circuit containing one cell, one
bulb, and a switch. Wire this on your
circuit board. Measure the voltage
across the cell and across the bulb.
What do you observe?
Minilab #2
Draw a circuit containing two cells in
series, one bulb, and a switch. Wire this
on your circuit board. What do you
observe happens to the bulb? Measure
the voltage across the battery and
across the bulb. What do you observe?
Minilab #3
Draw a circuit containing two cells in
series, two bulbs in series, and a
switch. Wire this on your circuit board.
What do you observe happens to the
bulbs? Measure the voltage across the
battery and across each bulb. What do
you observe?
Minilab #4
Draw a circuit containing two cells in
series, two bulbs in parallel, and a
switch. Wire this on your circuit board.
What do you observe happens to the
bulbs? Measure the voltage across the
battery and across each bulb. What do
you observe?
General rules
How does the voltage from a cell or
battery get dispersed in a circuit…
   when there is one component?
   when there are two components in series?
   when there are two components in
parallel?
Conductors
Conduct electricity easily.
Have high “conductivity”.
Have low “resistivity”.
Metals are examples.
Insulators
Don’t conduct electricity easily.
Have low “conductivity”.
Have high “resistivity”.
Rubber is an example.
Resistors
Resistors are devices put in circuits to
reduce the current flow.
Resistors are built to provide a
measured amount of “resistance” to
electrical flow, and thus reduce the
current.
Circuit components

Resistor
Sample problem
Draw a single loop circuit containing two resistors
and a cell. Draw voltmeters across each component.

V
V

V
Resisitance, R
Resistance depends on resistivity and
on geometry of the resistor.
R = L/A
   : resistivity (W m)
   L: length of resistor (m)
   A: cross sectional area of resistor (m2)
Unit of resistance: Ohms (W)
Sample problem
What is the resistivity of a substance which has a
resistance of 1000 W if the length of the material is
4.0 cm and its cross sectional area is 0.20 cm2?
Sample problem
What is the resistance of a mile of copper wire if the
diameter is 5.0 mm?
Ohm’s Law
Resistance in a component in a circuit
causes potential to drop according to
the equation:
DV = IR
   DV: potential drop (Volts)
   I: current (Amperes)
   R: resistance (Ohms)
Sample problem
Determine the current through a 333-W
resistor if the voltage across the resistor is
observed to be 1.5 V.
Sample problem
Draw a circuit with a AA cell attached to a light bulb
of resistance 4 W.
Determine the current through the bulb. (Calculate)
Ohmmeter
Measures Resistance.
Placed across resistor when no current
is flowing.

W
MiniLab #5
Set up your digital multimeter to measure
resistance. Measure the resistance of the
each light bulb on your board. Record the
results.
Wire the three bulbs together in series.
Measure the resistance of all three bulbs
together in the series circuit.
Wire the three bulbs together in parallel.
Measure the resistance of the parallel
arrangement.
MiniLab #5
Set up your digital multimeter to measure
resistance. Measure the resistance of the
each light bulb on your board. Record the
results.
Wire the three bulbs together in series.
Measure the resistance of all three bulbs
together in the series circuit.
Wire the three bulbs together in parallel.
Measure the resistance of the parallel
arrangement.
MiniLab #6
Measure the resistance of the different
resistors you have been given. Make a
table and record the color of the first
three bands (ignore the gold band) and
the resistance associated with the band
color. See if you can figure out the
code.
Resistor codes
Resistor color codes are read as follows:
resistors/resistor.htm
It is helpful to know this code, but you
will not be required to memorize it.
Ammeter
Measures Current.
Series Connection.
Low Resistance.

A
Power in General
P = W/t
P = DE/Dt
Units
   Watts
   Joules/second
Power in Electrical Circuits
P = I DV
   P: power (W)
   I: current (A)
   DV: potential difference (V)
P = I2R
P = (DV)2/R
Sample problem
How much current flows through a 100-W light bulb
connected to a 120 V DC power supply?

What is the resistance of the bulb?
Sample problem
If electrical power is 5.54 cents per kilowatt hour, how much
does it cost to run a 100-W light bulb for 24 hours?
Resistors in circuits
Resistors can be placed in circuits in a variety
of arrangements in order to control the
current.
Series arrangements always cause the
current in the circuit to be reduced.
Parallel arrangements can sometimes actually
increase the current, depending on how the
parallel branch is constructed.
Equivalent resistance
The equivalent resistance of a group of
resistors in a circuit is the value of a single
resistor that has the same resistance as the
resistor group.
Resistors in series have an equivalent
resistances.
Resistors in parallel have an equivalent
resistance calculated by adding the reciprocal
of the resistances to get the reciprocal of the
equivalent resistance.
Resistors in series

R1       R2     R3

Req = R1 + R2 + R3
Req = SRi
Resistors in parallel
R1
R2
R3

1/Req = 1/R1 + 1/R2 + 1/R3
1/Req = S(1/Ri )
MiniLab #7
What is the equivalent resistance of a 100-W, a 330-
W and a 560-W resistor when these are in a series
arrangement? (Draw, build a circuit, measure, and
calculate. Compare measured and calculated values).
Minilab #8
What is the equivalent resistance of a 100-W, a 330-
W and a 560-W resistor when these are in a parallel
arrangement? (Draw, build a circuit, measure, and
calculate. Compare measured and calculated values.)
Minilab #9
Draw and build an arrangement of
resistance that uses both parallel and series
arrangements for 5 or 6 resistors in your kit.
Calculate and then measure the equivalent
resistance. Compare the values.
Minilab #10: (Learning to use the DMM as
an ammeter without blowing a fuse.)
Draw an construct a circuit containing a cell and one
330-W resistor.
a) Measure the potential drop across the resistor
b) Measure the current through the resistor.
c) Does DV = IR?

I (A)        R(W)         DV (V)        DV (V)     difference (V)
(calc)     (measured)
Minilab #11: Ohm’s Law graph
Make a table of current and resistance data and graph the
data such that voltage is the slope of a best-fit line.
 Wire a circuit with a cell and one or more resistors.

Calculate and record the resistance. Measure and record
the corresponding current. Do this 8 times without
duplicating your resistance values. Since you have
only 4 unique resistors in your kit, you will have to use
resistor combinations in addition to single resistors to
 Rearrange the equation DV = IR so that DV is the slope

of a “linear” equation. Construct a graph from your data
that corresponds to this rearranged equation. Calculate
and clearly report the slope of the line. How does this
compare to the emf of 1.5 V for a D-cell?
Sample problem
Draw a circuit containing, in order (1) a 1.5 V cell, (2) a 100-W
resistor, (3) a 330-W resistor in parallel with a 100-W resistor (4)
a 560-W resistor, and (5) a switch.
Calculate the equivalent resistance.
Calculate the current through the cell.
Calculate the current through the 330-W resistor.
Kirchoff’s 1st Rule
Kirchoff’s 1st rule is also called the
“junction rule”.
The sum of the currents entering a
junction equals the sum of the currents
leaving the junction.
This rule is based upon conservation of
charge.
Sample problem
Find the current I4 (magnitude and direction).

3.0 A
I4

4.0 A        1.5 A
Kirchoff’s 2nd Rule
Kirchoff’s 2nd rule is also referred to as
the “loop rule”.
The net change in electrical potential in
going around one complete loop in a
circuit is equal to zero.
This rule is based upon conservation of
energy.
Sample problem
Use the loop rule to determine the potential drop across the
light bulb.

V
1.5 V         2.0 V            9.0 V

V
3.0 V
Announcements          11/23/2011
If you miss any days during the
current unit, you MUST see me about
making up the labs. I will hold makeup
sessions every morning.
Electrostatics exam corrections
Thursday, Friday this week. Must be
done by Friday. No exceptions.
Lunch bunch this week.
Minilab #12
• Draw and construct the following circuit.
• Measure the voltage supplied by the battery.
• Predict the currents I1, I2 and I3. Compare with measured
values.
• Apply Kirchoff’s 1st Rule to your current measurements.
• Predict the voltage across each resistor. Compare with
measured values.
• Apply Kirchoff’s 2nd Rule to your voltage measurements.

I2
I1                            I1
330 W           100 W
I3

560 W              I1

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