Transcript The Circuit

Electrical Circuits
~Moving Charge Put to Use
The Circuit
• All circuits, no matter how simple or complex, have one
thing in common, they form a complete loop.
• As mentioned before, circuits should have various circuit
elements in the loop.
Circuit Symbols
• Each circuit element has its own symbol.
• Common circuit symbols are shown below.
Wire
Battery
A Conductor
of Current
Switch
Source of DC
Charge Flow
Ammeter
Opens and
Closes Circuits
Resistor
Measures
Current
Voltmeter
Provides Resistance
to Current Flow
Measures
Voltage
More Circuit Symbols
• Here are some additional circuit symbols that you may see.
Capacitor
Diode
Stores Charge
on Plates
Potentiometer
Variable
Resistor
Only Allows Current
to Flow One Way
Junction
All Four Wires
Connect
AC Source
Provides AC
Current
Ground
Drains Excess
Charge Buildup
Crossing
Wires Only Cross
and do not Connect.
Circuit Diagrams
• Circuit diagrams use circuit symbols instead of
drawing an actual picture for each circuit.
• This simplifies and standardizes circuit pictures.
Circuit Picture
Circuit Diagram (Schematic)
Series Circuit
• Have you ever driven down a 1 lane road?
• You can keep moving until…
• If there is an accident all traffic stops, there is no other
road to follow.
Series Circuit
• A series circuit is similar to a one lane road,
current can flow in only one path.
• Even if you add a 2nd resistor in series, there is
still just 1 path.
R1
R2
Terminal Voltage
• Terminal voltage is the voltage supplied outside of the source
• This is ONLY the same as the EMF if there is no internal
resistance

Series Circuit
• One path means all components have the
same current
• What is the voltage drop across R1?
Vsource  VR1  VR 2
R1
V
I
VR1  IR1
VR 2  IR2
R2
Series Circuit
• How do we find Req?
Vseries  VR1  VR 2
I s R e q  I s R1  I s R2
Divide both sides by Is
R e q  R1  R2
R1
V
I
V
R2
Req
The Series Circuit (cont.)
• Every series configuration can be reduced to a single
value for resistance known as the equivalent resistance,
or Req.
• The formula for Req is as follows for series:
Req  R1  R2 
• This can be used as a step to solve for the current in the
circuit or the voltage across each resistor.
R1
I
Req
R2
Sample Problem (Series)
• A circuit is configured in series as shown below.
– What is the equivalent resistance (Req)?
10W
Req  R1  R2  R3
Req  10W  20W  30W
20W
6V
Req  60W
– What is the current through the circuit?
(Hint: Use Ohm’s Law.)
Req 
Veq
I eq
 I eq 
6V 

I eq 
 60W 
I eq  0.1A
Veq
30W
Ieq = 0.1A
Req
6V
60W
Sample Problem (Series) (cont.)
• We still have one question to ask. What are the voltages
across each resistor?
V
R   V  IR
I
Voltages across
– For the 10W Resistor:
V  IR
V   0.1A10W
V  1V
– For the 20W Resistor:
V  IR
V   0.1A 20W
resistors in series
add to make up
the total voltage.
V  2V
– For the 30W Resistor:
V  IR V   0.1A 30W V  3V
• What do you notice about the
voltage sum?
6V
Ieq = 0.1A
10W
20W
1V  2V  3V  6V
6V  Veq
30W
Series Circuit Summary
• Current is constant throughout the entire circuit.
I eq  I1  I 2 
• Resistances add to give Req.
Req  R1  R2 
• Voltages across each resistor add to give Veq.
Veq  V1  V2 
Devices that Make Use of the
Series Configuration
• Although not practical in every application, the
series connection is crucial as a part of most
electrical apparatuses.
– Switches
• Necessary to open and close entire circuits.
– Dials/Dimmers
• A type of switch containing a variable resistor
(potentiometer).
– Breakers/Fuses
• Special switches designed to shut off if current is too
high, thus preventing fires.
– Light Strands
• Prevents all bulbs from going out when a single
one burns out.
The Parallel Circuit (cont.)
• Parallel circuits are similar to rivers with branches in
them.
• The current from the river divides into multiple paths.
• After the paths, the water recombines into the same
amount of flowing water.
I eq  I1  I 2 
Ieq
Ieq
I1
I2
Parallel Circuit
• A parallel circuit is similar to a river that
branches, current can flow in multiple paths.
• Once the paths end, the total flow remains the
same
R1
R2
The Parallel Circuit
• Notice that the circuit branches out to each resistor,
allowing multiple paths for current to flow.
• If there are exactly two clear paths from the ends of one
resistor to the ends of the other resistor.
A break in one of the
branches of a parallel
circuit will not disable
current flow in the
remainder of the circuit.
Branch
X
R1
R2
X
Branch
Parallel Circuit
• How do we find Req a parallel circuit?
I parallel  I R1  I R 2
Vp
R eq

Vp
R1

Use Ohm’s law
Vp
1
1 1
 
R e q R1 R2
R2
Divide both sides by Vp
V
V
R1
R2
R2
V
Req
The Parallel Circuit (cont.)
• Notice how every resistor has a direct connection to the
DC source. This allows the voltages to be equal across
all resistors connected this way.
Veq  V1  V2 
• An equivalent resistance (Req) can also be found for
parallel configurations. It is as follows:
1
1 1
  
Req R1 R2
R1
R2
Req
Parallel Circuit video Clip
Sample Problem (Parallel)
• A circuit is configured in parallel as shown below.
– What is the equivalent resistance of the circuit?
1
1 1
1
  
Req R1 R2 R3
1
1
1
1



Req 30W 30W 60W
1
Req 
1
1 
 1




30
W
30
W
60
W


Req  12W
6V
6V
30W
30W
60W
12W
Sample Problem (Parallel)
• What is the current in the entire circuit?
Req 
Veq
I eq
 I eq 
Veq
Req
6V
I eq 
12W
I eq  0.5 A
• What is the current across each resistor?
The 30W Resistors
V
I
R
6V
The 60W Resistor
6V
I
30W
6V
I
60W
I  0.2 A
I  0.1A
30W
30W
60W
Parallel Circuit Summary
• There are several facts that you must always keep in
mind when solving parallel problems.
– Voltage is constant throughout the entire parallel circuit.
Veq  V1  V2 
– The Inverses of the Resistances add to give the inverse of Req.
1
1 1
  
Req R1 R2
– Current through each resistor adds to give Ieq.
I eq  I1  I 2 
– Make use of Ohm’s Law.
V
V
R   I   V  IR
I
R
Devices that Make Use of the
Parallel Configuration
• Although not practical or safe in every
application, the parallel circuit finds definite
use in some electrical apparatuses.
– Electrical Outlets
• Constant voltage is a must for appliances.
– Light Strands
• Prevents all bulbs from going out when a single
one burns out.
– Voltmeters
• Since voltage is constant in parallel, these
meters must be connected in this way.
Combination Circuits
• Parallel Paths: Must make a complete
loop through two resistors with out
touching any other component.
• Series Paths: Must form a path through
multiple resistors with out crossing an
intersection.
Combination Circuits
• Some circuits have series/parallel combinations
• These can be reduced using equivalent resistance
formulas.
• Now let’s solve a problem involving this circuit.
R2
R1
Series
R3
Parallel
R4
Sample Problem (Combo)
What is the equivalent resistance (Req) of the
circuit?
– First, we must identify the various combinations present.
Series
Parallel
Req  R1  R2 
Req  10W  30W
Req  40W
Parallel
25V
1
1 1
  
Req R1 R2
1
1
1


Req 20W 20W
Req  10W
Series
20W
10W
20W
30W
10W
40W
Sample Problem (Combo)
• The simplified circuit only shows the equivalent
resistances. Is the circuit now fully simplified?
• Now, we must identify the final configuration.
Series
Req  R1  R2
Req  40W  10W
Req  50W
25V
10W
40W
Parallel
25V
50W
Series
20W
10W
20W
30W
10W
40W
Sample Problem (Combo)
• The circuit is further simplified below. Can it be
simplified again?
• Now, the circuit is completely simplified.
• What is the current in the entire circuit?
Req 
Veq
I eq
 I eq 
Veq
25V
I eq 
50W
Req
I eq  0.5 A
Series
25V
10W
40W
50W
25V
50W
Lights demo
•
•
•
•
DC source with 3 lights in series
DC source with 3 lights in parallel
DC source with 2 lights in series 1 parallel
DC source with 1 lights in series 2 parallel
Conclusion
• In order to approach any circuit problem, you must know
the circuit symbols well.
• All the circuits that you will be given will be series,
parallel, or a combination of both that is solvable.
• Ultimately, keeping a working knowledge of the
properties of each circuit type is key. You may want to
make a note card that contains all of these facts.
15V
25V
20W
10W
30W
20W
15V
25V
30W
10W
30W
12μf
24μf
36μf
151W
130W
120W
131W
114W
140 W
220V
44W
117W
107W
126W
77W
113W
26W