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# Chapter 6 Parallel dc Circuits - PowerPoint PPT Presentation

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

Introductory Circuit Analysis

• 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.

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

Insert Fig 6.2

• 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

• 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.

• 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.

• For equal resistors in parallel:

Where N = the number of 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 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.

• 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.

• 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.

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

• 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.

• 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.

• 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.

• 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.

• 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.

• 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

• An open circuit can have a potential difference (voltage) across its terminal, but the current is always zero amperes.

• 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

• 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.

• 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.

• 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

• 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.

• 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.