Transcript Review - Worth County Schools

Introducing
Current and Direct
Current Circuits
Cells
cell
battery
Cells
Produce a voltage (called an EMF,
or Electromotive Force, or e).
EMF depends on chemistry of cell. A
perfect cell would produce a
terminal (or actual) voltage equal to
its EMF.
Terminal voltage is generally less
than the EMF.
Sample Circuit
V
light bulb
V
cell
Series Circuit
Only one path for the electricity
to travel through.
Good, because battery lasts
longer.
Bad, because the lights are
dimmer and if one blows, they
all blow.
Parallel Circuit
Multiple paths for the electricity
to flow through.
Good, because the lights are
brighter, and if one blows, the
others will remain lit.
Bad, because the battery will
be drained faster.
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.
Resistivity / Conductivity
Depends on the identity
of the material, not its
shape, size, or
configuration.
Available in tables of
data.
Resistors
Devices put in circuits to
reduce the current flow.
Built to provide a
measured amount of
“resistance” to electrical
flow, and thus reduce the
current.
Resistors
V
V
V
Ohm’s Law
Resistance in circuit
causes potential to
drop
V = IR
Voltmeter
Measures voltage.
Placed across a load or power
source when current is flowing
V
V
cell
light bulb
Ohmmeter
Measures Resistance
Placed across resistor when no
current is flowing
W
Ammeter
Measures Current
Series Connection
Low Resistance
A
Power in Electrical Circuits
P = I V
P: power (W)
 I: current (A)
 V: potential difference (V)

2
IR
P =
P = V2/R
Electrical Circuit Symbols
Electrical circuits often contain one or more
resistors grouped together and attached to
an energy source, such as a battery.
The following symbols are often used:
Ground
+ - + - + - + -
Battery
+
-
Resistor
Resistances in Series
Resistors are said to be connected in series when there
is a single path for the current.
I
R1
VT
R2
R3
Only one current
For series
connections:
The current I is the same for
each resistor R1, R2 and R3.
The energy gained through E is
lost through R1, R2 and R3.
The same is true for voltages:
I = I 1 = I 2 = I3
= V1 + V2 + V3
VT
Equivalent Resistance:
Series
The equivalent resistance Re of a number of
resistors connected in series is equal to the sum of
the individual resistances.
VT = V1 + V2 + V3 ; (V = IR)
I
R1
VT
R2
R3
Equivalent Resistance
ITRe = I1R1+ I2R2 + I3R3
But . . . IT = I1 = I2 = I3
Re = R1 + R2 + R3
Example 1: Find the equivalent resistance Re.
What is the current I in the circuit?
Re = R1 + R2 + R3
2W
3W 1W
12 V
Re = 3 W + 2 W + 1 W = 6 W
Equivalent Re = 6 W
The current is found from Ohm’s law: V = IRe
V 12 V
I

Re 6 W
I=2A
Example 1 (Cont.): Show that the voltage drops
across the three resistors totals the 12-V emf.
2W
3W 1W
12 V
Re = 6 W
I=2A
Current I = 2 A same in each R.
V1 = IR1; V2 = IR2; V3 = IR3
V1 = (2 A)(1 W) = 2 V
V1 + V2 + V3 = VT
V1 = (2 A)(2 W) = 4 V
2 V + 4 V + 6 V = 12 V
V1 = (2 A)(3 W) = 6 V
Check !
Parallel Connections
Resistors are said to be connected in parallel when there
is more than one path for current.
Parallel Connection:
2W
4W
6W
Series Connection:
2W
4W
6W
For Parallel Resistors:
V2 = V4 = V6 = VT
I 2 + I 4 + I 6 = IT
For Series Resistors:
I 2 = I 4 = I 6 = IT
V2 + V4 + V6 = VT
Equivalent Resistance:
Parallel
VT = V1 = V2 = V3
I T = I1 + I 2 + I3
Ohm’s law:
Parallel Connection:
VT
V
I
R
VT V1 V2 V3
 

Re R1 R2 R3
The equivalent resistance for
Parallel resistors:
R1
R2
R3
1
1
1
1
 

Re R1 R2 R3
N
1
1

Re i 1 Ri
Example 3. Find the equivalent resistance
Re for the three resistors below.
N
1
1

Re i 1 Ri
VT
R1
2W
R2
4W
R3
6W
1
1
1
1
 

Re R1 R2 R3
1
1
1
1



 0.500  0.250  0.167
Re 2 W 4 W 6 W
1
 0.917;
Re
1
Re 
 1.09 W
0.917
Re = 1.09 W
For parallel resistors, Re is less than the least Ri.
Example 3 (Cont.): Assume a 12-V emf is
connected to the circuit as shown. What is
the total current leaving the source of emf?
VT
R1
2W
R2
4W
R3
6W
VT = 12 V; Re = 1.09 W
V1 = V2 = V3 = 12 V
IT = I1 + I2 + I3
12 V
Ohm’s Law:
V
I
R
VT
12 V
Ie 

Re 1.09 W
Total current: IT = 11.0 A
Example 3 (Cont.): Show that the current
leaving the source IT is the sum of the
currents through the resistors R1, R2, and R3.
VT
R1
2W
R2
4W
R3
6W
V1 = V2 = V3 = 12 V
IT = I1 + I2 + I3
12 V
12 V
I1 
6A
2W
IT = 11 A; Re = 1.09 W
12 V
I2 
3A
4W
6 A + 3 A + 2 A = 11 A
12 V
I3 
2A
6W
Check !
Short Cut: Two Parallel
Resistors
The equivalent resistance Re for two parallel resistors
is the product divided by the sum.
1
1
1
  ;
Re R1 R2
Example:
VT
R1
6W
R2
3W
R1 R2
Re 
R1  R2
(3 W)(6 W)
Re 
3W  6 W
Re = 2 W
Series and Parallel
Combinations
In complex circuits resistors are often connected in both
series and parallel.
R1
In such cases, it’s best to use
rules for series and parallel
resistances to reduce the
circuit to a simple circuit
containing one source of emf
and one equivalent resistance.
VT R2
VT
R3
Re
Example 4. Find the equivalent resistance for
the circuit drawn below (assume VT = 12 V).
4W
VT
3W
R3,6
6W
(3 W)(6 W)

 2W
3W  6 W
Re = 4 W + 2 W
Re = 6 W
4W
12 V
2W
12 V
6W
Example 3 (Cont.) Find the total current IT.
Re = 6 W
4W
VT
3W
6W
VT 12 V
I

Re 6 W
IT = 2.00 A
4W
12 V
2W
12 V
IT
6W
Example 3 (Cont.) Find the currents and the
voltages across each resistor.
I4 = IT = 2 A
4W
VT
3W
6W
V4 = (2 A)(4 W) = 8 V
The remainder of the voltage: (12 V – 8 V = 4 V) drops
across EACH of the parallel resistors.
V3 = V6 = 4 V
This can also be found from V3,6
= I3,6R3,6 = (2 A)(2 W)
(Continued . . .)
Example 3 (Cont.) Find the currents and voltages
across each resistor.
V4 = 8 V
V6 = V3 = 4 V
V3 4 V
I3 

R3 3 W
V6 4 V
I6 

R6 6 W
I3 = 1.33 A
4W
VT
I6 = 0.667 A
3W
I4 = 2 A
Note that the junction rule is satisfied:
SI (enter) = SI (leaving)
I T = I4 = I 3 + I 6
6W
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 )
Kirchoff’s
st
1
Rule
Junction rule.
The sum of the currents
entering a junction equals
the sum of the currents
leaving the junction.
Conservation of…

charge.
Kirchoff’s
nd
2
Rule
Loop rule.
The net change in electrical
potential in going around
one complete loop in a
circuit is equal to zero.
Conservation of

energy.