Transcript Circuits - Effingham County Schools

Current Electricity:
Direct Current Circuits, Ohm’s Law, Resistance, Electric
Power, Equivalent Resistance, Kirchoff’s Rules
Current
 Current is defined as the flow
of positive charge
 I = Q/t
 I is current in Amperes (A)
 Q is charge in Coulombs (C)
 t is time in seconds (s)
 In a normal electric circuit,
electrons move to carry charge
– the current is opposite from
the movement of electrons
Practice #1
 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, which way is the
current?
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?
Cells
 Cells convert chemical energy into electrical energy
 The potential difference (voltage) provided by a cell is
called its electromotive force (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!
Cells
cell
battery
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
 Practice Problem #2:
 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.
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:
 Voltmeter: (measures
voltage)
 Wire:
 Switch:
 Ohmmeter: (measures
resistance)
Ω
 Ammeter (measures
current)
Circuit Practice - #3
 Draw a single loop circuit
that contains a cell, a light
bulb, and a switch. Name
the components.
Sample problem
Draw a single loop circuit that contains a
cell, a light bulb, and a switch. Name the
components
bulb
cell
switch
#4
 Now put a voltmeter in
the circuit so it reads the
potential difference across
the bulb
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
I
1/3 I
1/3 I
1/3 I
I
1/3 I Three bulbs in parallel
1/3 I
Practice # 5-6
5. Draw a circuit with one
cell and two bulbs in
series.
6. Draw a circuit having a
cell and four bulbs.
Exactly two of the bulbs
must be in parallel.
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.
http://www.youtube.com/watch?v=e8v
JlTEvbUk&feature=youtu.be
Conductors & Insulators
Conductors
Insulators
 Conduct electricity easily
 Don’t conduct electricity easily
 Have high “conductivity”
 Have low “conductivity”
 Have low “resistivity”
 Have high “resistivity”
 Metals are examples
 Rubber is an example
 Wires are made of conductors
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
#7
 Draw a single loop circuit containing two resistors and a
cell. Draw voltmeters across each component.
Sample problem
Draw a single loop circuit containing two resistors
and a cell. Draw voltmeters across each component.
V
V
V
Resistance, R
 Resistance depends on resistivity
and on geometry of the resistor
 R = ρL/A
 ρ : resistivity (Ωm) from the material
 L: length of resistor (m)
 A: cross sectional area of resistor
(m2)
 Unit of resistance: Ohms (Ω)
Practice #8
 What is the resistivity of a substance which has resistance
of 1000 Ω if the length of the material is 4.0 cm and its
cross sectional area is 0.20 cm2?
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?
#9
 What is the resistance of a mile of copper wire if the
diameter is 10.0 mm?
 (resistivity of copper is 1.72 x 10-8 Ωm)
Sample problem
What is the resistance of a mile of copper wire if the
diameter is 10.0 mm?
Ohm's Law
 Resistance in a component in a circuit causes potential to
drop according to the equation:
 ΔV = IR
 ΔV : potential drop (Volts)
 I: current (Amperes)
 R: resistance (Ohms)
Practice #10
 Determine the current through a 333 Ω resistor if the
voltage across the resistor is observed to be 1.5 V.
Sample problem
Determine the current through a 333-W
resistor if the voltage across the resistor is
observed to be 1.5 V.
Practice #11
 Draw a circuit with a AA cell attached to a light bulb of
resistance 4 Ω.
 Determine the current through the bulb.
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
Ammeter
 An ammeter measures current
 It is placed in the circuit in a series connection
 An ammeter has very low resistance, and does not
contribute significantly to the total resistance of the
circuit
Power
In General
In Electrical Circuits
 P = W/t
 P=IΔV
 P: Power (W)
 I: Current (A)
 Δ V: Potential difference (V)
 P = I2R
 P = ΔE/Δt
 Units:
 Watts
 Joules/second
 P = (Δ V)2/R
Practice #12
 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
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?
#13
 If electrical energy (power x time) is 5.54 cents per
kilowatt hour, how much does it cost to run a 100-W light
bulb for 24 hours?
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
 Arranging resistors in series increases the resistance and
causes the current to be reduced
 Arranging the resistors in parallel reduces the resistance
and causes the current to increase
 The overall resistance of a specific grouping of resistors is
referred to as the equivalent resistance
Equivalent Resistance
In Series
In Parallel
 Req = R1 + R2 + R3…
 1/Req = 1/R1 + 1/R2 + 1/R3…
 ΣReq = Ri
 1/Req = Σ(1/Ri)
Kirchoff's
st
1
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
Practice Problem #15
 Find the current I4 (magnitude
and direction)
3.0 A
I4
4.0 A
1.5 A
Kirchoff's
nd
2
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 the conservation of energy
Practice Problem #16
 Use the loop rule to determine the potential drop across
the light bulb.
Capacitors in Circuits
+Q
-Q
+Q
-Q
Equivalent Capacitance
C1
C2
C3
series
Charge is
same on all
capacitors in
series
arrangement.
1/Ceq = 1/C1+ 1/C2 + 1/C3
Equivalent Capacitance
C1
C2
C3
parallel
Voltage is
same on all
capacitors in
parallel
arrangement.
Ceq = C1+ C2 + C3
http://www.youtube.com/watch?v=BQb
OWBnKy9M&feature=youtu.be
Mini-Lab J
 Draw and construct the following circuit.
 Predict all 3 currents. Apply Kirchoff’s 1st Rule to your
current measurements
 Measure the voltage across all components. Apply
Kirchoff’s 2nd Rule to your voltage measurements.
Mini-Lab K
 Draw and construct a circuit containing a cell and one
330-Ω resistor.
 Measure the potential drop across the resistor
 Measure the current through the resistor
 Does ΔV = IR?
I (A)
R(Ω)
ΔV(V)
calculated
ΔV(V)
Measured
Difference
(V)
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. You will have to use
resistor combinations in addition to single resistors.
 Rearrange the equation V = IR so that V 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 a 1.5 V for a D-cell?
Circuit Mini-Lab A
 Draw a circuit containing one cell, one bulb, and a switch.
Wire this circuit. Measure the voltage across the cell and
across the bulb. What do you observe?
Mini-Lab B
 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:


With two cells instead of one?
When opening and closing the switch?
 Measure the voltage across the battery and across the bulb.
What do you observe?
Mini-Lab C
 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 when you
unscrew one of them?
 Measure the voltage across the battery and across each
bulb. What do you observe?
Mini-Lab D
 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 when you
unscrew one bulb?
 Measure the voltage across the battery and across each
bulb. What do you observe?
General Rules for Circuits
 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?
Mini-Lab E
 Set up your digital multi-meter to measure resistance.
Measure the resistance of each light bulb on your board.
Record the results.
 Wire three bulbs together in series, and draw this
arrangement. Measure the resistance of all three bulbs
together in the series circuit. How does this compare to
the resistance of the individual bulbs?
 Wire three bulbs together in parallel, and draw this
arrangement. Measure the resistance of all three bulbs
together in the parallel arrangement. How does this
compare to the resistance of the individual bulbs?
Mini-Lab F
 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 silver/gold band) and the
resistance associated with the band color. See if you can
figure out the code.
Resistor codes
 Resistor codes are read as follows:
 It is helpful to know the code, but you will not be
required to memorize it
Mini-Lab G
 What is the equivalent resistance of a 100-Ω, a 330- Ω,
and a 82- Ω resistor when these are in a series
arrangement?
 Draw the circuit
 Build the circuit
 Measure values
 Calculate and compare measured and calculated values
Mini-Lab H
 What is the equivalent resistance of a 100-Ω, a 330-Ω,
and a 82-Ω resistor when these are in a parallel
arrangement?
 Draw
 Build the circuit
 Measure
 Calculate and compare values
Mini-Lab I
 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.
#14
 Draw a circuit containing, in order (1) a 1.5 V cell, (2) a 68-
Ω resistor, (3) a 330-Ω resistor in parallel with a 100-Ω
resistor, (4) an 82-Ω resistor, and (5) a switch.
 Calculate the equivalent resistance
 Calculate the current through the cell
 Calculate the current through the 330-Ω resistor