Chapter 6 – Parallel Circuits Introductory Circuit Analysis Robert L. Boylestad 6.1 - Introduction There are two network configurations – series and parallel In Chapter 5
Download
Report
Transcript Chapter 6 – Parallel Circuits Introductory Circuit Analysis Robert L. Boylestad 6.1 - Introduction There are two network configurations – series and parallel In Chapter 5
Chapter 6 – Parallel Circuits
Introductory Circuit Analysis
Robert L. Boylestad
6.1 - Introduction
There are
two network configurations – series
and parallel
In Chapter 5 we covered a series network, and in
this chapter we will cover the parallel circuit and
all the methods and laws associated with it
6.2 - Parallel Elements
Two
elements, branches, or networks are in parallel if
they have two points in common as in the figure below
Insert Fig 6.2
6.3 - Total Conductance and
Resistance
For parallel elements, the total conductance is
the sum of the individual conductances.
GT = + G1 + G2 + G3 +… + Gn
As the number of resistors in parallel increases, the
input current level will increase for the same applied
voltage
This is the opposite effect of increasing the number
of resistors in a series circuit
Total Conductance and Resistance
Since G = 1/R the total resistance for a network can
be determined by the equation below
Note that the equation is for 1 divided by the total
resistance rather than the total resistance
Once the right side of the equation has been
determined, it is necessary to divide the result into 1 to
determine the total resistance
Total Conductance and Resistance
The
total resistance of a parallel resistor is always less than
the value of the smallest resistor
Additionally, the wider the spread in numerical value between two
parallel resistors, the closer the total resistance will be to the smaller
resistor
The equation becomes significantly easier to apply for equal resistors
in parallel
Total
resistance of N parallel resistors of equal value is the resistance
of one resistor divided by the number (N) of parallel elements
Total Conductance and Resistance
The total resistance of
two resistors is the
product of the two divided by their sum
The
equation was developed to reduce the effects of
the inverse relationship when determining RT
Total Conductance and Resistance
Parallel elements can be interchanged without
changing the total resistance or input current
For parallel resistors, the total resistance will
always decrease as additional elements are
added in parallel
6.4 - Parallel Circuits
Total resistance is determined
by RT = R1 R2 / (R1 + R2 )
and the source current by Is = E / RT .
The subscript s will be used to denote a property of the
source
The voltage across parallel
elements is the same
V1 = V2 = E
Voltage across resistor 1 is equal to the voltage across
resistor 2
Parallel Circuits
For single-source parallel networks, the source
current (I ) is equal to the sum of the individual
branch currents
s
Is = I1 + I2
6.5 - Kirchhoff’s Current Law
Kirchhoff’s voltage law provides an important relationship
among voltage levels around any closed loop of a network
Now consider Kirchhoff’s current law (KCL)
Kirchhoff’s current law states that the algebraic sum of the
currents entering and leaving an area, system, or junction is
zero
The sum of the current entering an area, system or junction
must equal the sum of the current leaving the area, system,
or junction
Ientering
= Ileaving
Kirchhoff’s Current Law
Most common application of the law will be at the junction
of two or more paths of current flow
Determining whether a current is entering or leaving a
junction is sometimes the most difficult task
One approach to understanding the flow is to picture
yourself as standing on the junction point and treating the
path currents as arrows
If the arrow appears to be heading toward you, the current
is entering the junction
If you see the tail of the arrow as it travels down its path away
from you, the current is leaving the junction
6.6 - Current Divider Rule
The current
divider rule (CDR) will determine how the
current entering a set of parallel branches will split
between the elements
For two parallel elements of equal value, the current will
divide equally
For parallel elements with different values, the smaller the
resistance, the greater the share of input current
For parallel elements of different values, the current will split
with a ratio equal to the inverse of their resistor values
Current Divider Rule
Current seeks the path of least resistance
The
current entering any number of parallel resistors divides
into these resistors as the inverse ratio of their ohmic value
6.7 - Voltage Sources in Parallel
Voltage sources are placed in parallel only if they
have the same voltage rating
The purpose for placing two or more batteries in parallel
would be to increase the current rating
The formula to determine the total current is:
Is = I1 + I2 +… IN
at the same terminal voltage
Voltage Sources in Parallel
Two batteries of different terminal voltages
placed in parallel
When two batteries of different terminal voltages are
placed in parallel, the larger battery tries to drop
rapidly to the lower supply
The result is the larger battery quickly discharges to
the lower voltage battery, causing the damage to both
batteries
6.8 - Open and Short Circuits
An open circuit can have a potential difference (voltage)
across its terminal, but the current is always zero
amperes
Two isolated terminals not connected by any element:
Open and Short Circuits
A short circuit can carry a current of a level determined
by the external circuit, but the potential difference
(voltage) across its terminals is always zero volts
Insert Fig 6.44
6.9 - Voltmeters: Loading Effect
Voltmeters are always placed across an element to
measure the potential difference
The resistance of two parallel resistors will always be less
than the resistance of the smallest resistor
A DMM has internal resistance which will alter, somewhat,
the network being measured
The loading of a network by the insertion a meter is not to
be taken lightly, especially if accuracy is a primary
consideration
Voltmeters: Loading Effect
A good
practice is to always check the meter resistance level
against the resistive elements of the network before making
a measurement
Most DMMs have internal resistance levels in excess of 10
MW on all voltage scales
Internal resistance of VOMs is sensitive to the scale chosen
Internal resistance is determined by multiplying the maximum
voltage of the scale setting by the ohm/volt ( / V) rating of the
meter, normally found at the bottom of the face of the meter
6.10 - Troubleshooting
Techniques
Troubleshooting is
a process by which acquired
knowledge and experience are employed to localize
a problem and offer or implement a solution
Experience and a clear understanding of the basic
laws of electrical circuits is vital
First step should always be knowing what to expect
6.11 - Applications
Car system
The electrical system on a car is essentially a parallel
system
Parallel computer bus connections
The bus connectors are connected in parallel with
common connections to the power supply, address
and data buses, control signals, and ground
Applications
House wiring
Except in some very special circumstances the basic
wiring of a house is done in a parallel configuration
Each parallel branch, however, can have a
combination of parallel and series elements
Each branch receives a full 120 V or 208 V, with the
current determined by the applied load