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Chapter 6 – Parallel dc Circuits. Introductory Circuit Analysis Robert L. Boylestad. 6.1 - Introduction. There are two network configurations – series and parallel.

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Chapter 6 parallel dc circuits

Chapter 6 – Parallel dc Circuits

Introductory Circuit Analysis

Robert L. Boylestad


6 1 introduction
6.1 - Introduction

  • There are two network configurations – series and parallel.

  • In Chapter 5 we covered a series network. In this chapter we will cover the parallel circuit and all the methods and laws associated with it.


6 2 parallel resistors
6.2 – Parallel Resistors

  • Two elements, branches, or circuits are in parallel if they have two points in common as in the figure below

Insert Fig 6.2


Parallel resistors
Parallel Resistors

  • For resistors in parallel, the total resistance is determined from

  • Note that the equation is for the reciprocal of RT rather than for RT.

    • Once the right side of the equation has been determined, it is necessary to divide the result into 1 to determine the total resistance


Parallel resistors1
Parallel Resistors

  • For parallel elements, the total conductance is the sum of the individual conductance values.

    • 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.


Parallel resistors2
Parallel Resistors

  • The total resistance of any number of parallel resistors can be determined using

  • The total resistance of parallel resistors is always less than the value of the smallest resistor.


Parallel resistors3
Parallel Resistors

  • For equal resistors in parallel:

    Where N = the number of parallel resistors.


Parallel resistors4
Parallel Resistors

  • A special case: 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


Parallel resistors5
Parallel Resistors

  • Parallel resistors can be interchanged without changing the total resistance or input current.

  • For parallel resistors, the total resistance will always decrease as additional parallel elements are added.


6 3 parallel circuits
6.3 – Parallel Circuits

  • Voltage is always the same across parallel elements.

    V1 = V2 = E

    The voltage across resistor 1 equals the voltage across resistor 2, and both equal the voltage supplies by the source.


Parallel circuits
Parallel Circuits

  • For single-source parallel networks, the source current (Is) is equal to the sum of the individual branch currents.

  • For a parallel circuit, source current equals the sum of the branch currents. For a series circuit, the applied voltage equals the sum of the voltage drops.


Parallel circuits1
Parallel Circuits

  • For parallel circuits, the greatest current will exist in the branch with the lowest resistance.


6 4 power distribution in a parallel circuit
6.4 – Power Distribution in a Parallel Circuit

  • For any resistive circuit, the power applied by the battery will equal that dissipated by the resistive elements.

  • The power relationship for parallel resistive circuits is identical to that for series resistive circuits.


6 5 kirchhoff s current law
6.5 - Kirchhoff’s Current Law

  • Kirchhoff’s voltage law provides an important relationship among voltage levels around any closed loop of a network.

  • Kirchhoff’s current law (KCL) 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.


Kirchhoff s current law
Kirchhoff’s Current Law

  • Most common application of the law will be at the junction of two or more paths of current.

  • Determining whether a current is entering or leaving a junction is sometimes the most difficult task.

    • If the current arrow points toward the junction, the current is entering the junction.

    • If the current arrow points away from the junction, the current is leaving the junction.


6 6 current divider rule
6.6 – Current Divider Rule

  • The current divider rule (CDR) is used to find the current through a resistor in a parallel circuit.

  • General points:

    • 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.



6 7 voltage sources in parallel
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 is to increase the current rating.

    • The formula to determine the total current is:

    • at the same terminal voltage.


Voltage sources in parallel
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
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.


Open and short circuits
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 voltmeter loading effects
6.9 – Voltmeter Loading Effects

  • Voltmeters are always placed across an element to measure the potential difference.

    • The resistance of parallel resistors will always be less than the resistance of the smallest resistor.

    • A DMM has internal resistance which may alter the resistance of the network under test.

    • The loading of a network by the insertion of a meter is not to be taken lightly, especially if accuracy is a primary consideration.


Voltmeter loading effects
Voltmeter Loading Effects

  • A good practice is to always check the meter resistance 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.

  • The internal resistance of a VOM depends on the scale chosen.

    • Internal resistance is determined by multiplying the maximum voltage of the scale setting by the ohm/volt ( / V) ratingof the meter, normally found at the bottom of the face of the meter.


6 11 troubleshooting techniques
6.11 – 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 13 applications
6.13 – 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
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.


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