Download Electrical Circuits

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.
• These vary depending on the design of the circuit.
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 employ the use of the circuit symbols as
opposed to drawing an actual picture for each circuit.
• This simplifies and standardizes circuit pictures.
• Compare the picture below to the circuit diagram below.
Circuit Picture
Circuit Diagram (Schematic)
The Series Circuit
• Look at the circuit below. Two resistors are connected in
a series configuration.
• Notice there is only one path for current to flow. There
are no branches in the circuit, which would allow charge
to take multiple paths.
• Since there is only one path, the current everywhere in
the circuit is constant, even through the resistors.
I eq  I1  I 2 
A break at any point in
the circuit will result in the
stoppage of current flow.
R1
R2
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
Req
R2
Sample Problem (Series)
• A circuit is configured in series as shown below.
– What is the equivalent resistance (Req)?
Req  R1  R2  R3
Req  10W  20W  30W
60W
6V
Req  60W
– What is the current through the circuit?
10W
(Hint: Use Ohm’s Law.)
Ieq = 0.1A
Req 
Veq
I eq
 I eq 
6V 

I eq 
 60W 
I eq  0.1A
Veq
Req
20W
6V
30W
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
• There are several facts that you must always keep in
mind when solving series problems.
– 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 
– Make use of Ohm’s Law.
V
V
R   V  IR  I 
I
R
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.
– Ammeters
• Since current is constant in series, these currentmeasuring devices must be connected in that
configuration as well.
The Parallel Circuit
• Look at the circuit below. The resistors have been
placed in a parallel configuration.
• Notice that the circuit branches out to each resistor,
allowing multiple paths for current to flow.
• One way to test if two resistors are in parallel is to see 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
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
The Parallel Circuit (cont.)
•
•
•
•
Do you like rivers?
Parallel circuits are kind of like rivers with branches in them.
Is the current in each branch equal to the total current of the river?
No, the total current is equal to the sum of the current in each
branch.
• Thus, the individual currents add to form the total current.
I eq  I1  I 2 
Ieq
Ieq
I1
I2
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.
R
V
V
 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
• Some circuits, such as the one shown below, have
series/parallel combinations in their configurations.
• Many of these can be reduced using equivalent
resistance formulas, while some cannot.
• Do you see the combinations within this circuit?
• Now let’s solve a problem involving this circuit.
R1
R2
Series
R3
Parallel
R4
Sample Problem (Combo)
• A combination circuit is shown below.
• 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?
• No, we must identify the final configuration. What is it?
Series
• It’s a series configuration.
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?
• No, 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
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.