Presentation on theme: "Chapter 5 – Series dc Circuits"— Presentation transcript:
1Chapter 5 – Series dc Circuits Introductory Circuit AnalysisRobert L. Boylestad1
25.1 - IntroductionTwo types of current are readily available, direct current (dc) and sinusoidal alternating current (ac)We will first consider direct current (dc)Insert Fig 5.12
3IntroductionIf a wire is an ideal conductor, the potential difference (V) across the resistor will equal the applied voltage of the battery.V (volts) = E (volts)Current is limited only by the resistor (R). The higher the resistance, the less the current.3
45.2 - Series ResistorsThe total resistance of a series configuration is the sum of the resistance levels.The more resistors we add in series, the greater the resistance (no matter what their value).Current through all resistors in a series circuit is the same.4
5Series Resistors When series resistors have the same value, Where N = the number of resistors in the string.The total series resistance is not affected by the order in which the components are connected.5
65.3 – Series Circuits Total resistance (RT) is all the source “sees.” Once RT is known, the current drawn from the source can be determined using Ohm’s law:Since E is fixed, the magnitude of the source current will be totally dependent on the magnitude of RT .6
7Series CircuitsThe polarity of the voltage across a resistor is determined by the direction of the current.When measuring voltage, start with a scale that will ensure that the reading is lower than the maximum value of the scale. Then work your way down until a reading with the highest level of precision is made.7
85.4 – Power Distribution in a Series Circuit The power applied by the dc supply must equal that dissipated by the resistive elements.
13Using voltmeters to measure the voltages across the resistors
14Protoboard with areas of conductivity defined using two different approaches.
15Two setups for a network on a protoboard with yellow leads added to each configuration to measure voltage V3 with a voltmeter.
165.5 - Voltage Sources in Series Voltage sources can be connected in series to increase or decrease the total voltage applied to the system.Net voltage is determined by summing the sources having the same polarity and subtracting the total of the sources having the opposite polarity.8
17Reducing series dc voltage sources to a single source.
18Series connection of dc supplies: (a) four 1 Series connection of dc supplies: (a) four 1.5 V batteries in series to establish a terminal voltage of 6 V; (b) incorrect connections for two series dc supplies; (c) correct connection of two series supplies to establish 60 V at the output terminals.
195.6 - Kirchhoff’s Voltage Law Kirchhoff’s voltage law (KVL) states that the algebraic sum of the potential rises and drops around a closed loop (or path) is zero.9
20Kirchhoff’s Voltage Law The applied voltage of a series circuit equals the sum of the voltage drops across the series elements:The sum of the rises around a closed loop must equal the sum of the drops.The application of Kirchhoff’s voltage law need not follow a path that includes current-carrying elements.When applying Kirchhoff’s voltage law, be sure to concentrate on the polarities of the voltage rise or drop rather than on the type of element.Do not treat a voltage drop across a resistive element differently from a voltage drop across a source.10
21Applying Kirchhoff’s voltage law to a series dc circuit. E = V1 + V2Applying Kirchhoff’s voltage law to a series dc circuit.
255.7 – Voltage Division in a Series Circuit The voltage across the resistive elements will divide as the magnitude of the resistance levels.The greater the value of a resistor in a series circuit, the more of the applied voltage it will capture.Voltage Divider Rule (VDR)The VDR permits determining the voltage levels of a circuit without first finding the current.12
26Voltage Division in a Series Circuit The voltage across a resistor in a series circuit is equal to the value of the resistor times the total impressed voltage across the series elements divided by the total resistance of the series elements.The rule can be extended to voltage across two or more series elements if the resistance includes total resistance of the series elements that the voltage is to be found across.13
27How the voltage will divide across series resistive elements
28How the voltage will divide across series resistive elements
29The largest of the series resistive elements will capture the major share of the applied voltage.
325.8 - Interchanging Series Elements Elements of a series circuit can be interchanged without affecting the total resistance, current, or power to each elementIn the Figures below, resistors 2 and 3 are interchanged without affecting the total resistanceInsert Fig 5.19Insert Fig 5.2011
33Voltage sources and grounds 5.9 - NotationVoltage sources and groundsGround symbolVoltage source symbol14
34Notation Double-subscript notation Because voltage is an “across” variable and exists between two points, the double-subscript notation defines differences in potential.The double-subscript notation Vab specifies point a as the higher potential. If this is not the case, a negative sign must be associated with the magnitude of Vab .The voltage Vab is the voltage at point (a) with respect to point (b).15
35Notation Single-subscript notation The single-subscript notation Va specifies the voltage at point a with respect to ground (zero volts). If the voltage is less than zero volts, a negative sign must be associated with the magnitude of Va .Va = +10 VVb = + 4 VVab = 10 – 4 = 6 V16
36Notation Vab = Va – V b General Relationship If the voltage at points a and b are known with respect to ground, then the voltage Vab can be determined using the following equation:Vab = Va – V b17
37Va = 10 V and Vab = 4 VVb = +6 V and Vbc = 20 V Vc = -14 V
395.10 – Voltage Regulation and the Internal Resistance of Voltage Sources The ideal voltage source has no internal resistance and an output voltage of E volts with no load or full load.Every practical voltage source (generator, battery, or laboratory supply) has some internal resistance.Voltage across the internal resistance lowers the source output voltage when a load is connected.For any chosen interval of voltage or current, the magnitude of the internal resistance is given byRint = VL / IL18
40(a) Sources of dc voltage; (b) equivalent circuit.
41Demonstrating the effect of changing a load on the terminal voltage of a supply.
43Voltage Regulation and the Internal Resistance of Voltage Sources For any supply, ideal conditions dictate that for a range of load demand (IL), the terminal voltage remains fixed in magnitude.If a supply is set at 12 V, it is desirable that it maintain this terminal voltage, even though the current demand on the supply may vary.Voltage regulation (VR) characteristics are measures of how closely a supply will come to maintaining a supply voltage between the limits of full-load and no-load conditions.19
44Voltage Regulation and the Internal Resistance of Voltage Sources Ideal conditions: VFL = VNL and VR = 0%The lower the voltage regulation, the less the variation in terminal voltage with changes in load20
45Defining the properties of importance for a power supply.
46VNL = 20.1 V and VFL = VVR = (20.1 – 18.72)/(18.72) = = 7.37%
475.11 – Loading Effects of Instruments For an up-scale (analog meter) or positive (digital meter) reading an ammeter must be connected with current entering the positive terminal and leaving the negative terminalAmmeters are placed in series with the branch in which the current is to be measured21
48Loading Effects of Instruments Voltmeters are always hooked up across the element for which the voltage is to be determinedFor a double-script notation: Always hook up the red lead to the first subscript and the black lead to the second.For a single-subscript notation: Hook up the red lead to the point of interest and the black lead to the ground22
49Including the effects of the internal resistance of an ammeter: (a) 2 mA scale; (b) 2 A scale.
50Applying an ammeter, set on the 2 mA scale, to a circuit with resistors in the kilohm range: (a) ideal; (b) practical.
515.13 – Applications Holiday lights Holiday lights are connected in series if one wire enters and leaves the casing.If one of the filaments burns out or is broken, all of the lights go out unless a fuse link is used.A fuse link is a soft conducting metal with a coating on it that breaks down if the bulb burn out, causing the bulb to be by-passed, thus only one bulb goes out.23
56Applications Microwave oven A series circuit can be very useful in the design of safety equipment.In a microwave, it is very dangerous if the oven door is not closed or sealed properly. Microwaves use a series circuit with magnetic switches on the door to ensure that the door is properly closed.Magnetic switches are switches where the magnet draws a magnetic conducting bar between two conductors to complete the circuit.24