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## Resistors in Series Introduction

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**Resistors in SeriesIntroduction**Two types of current are readily available, direct current (dc) and sinusoidal alternating current (ac) We will first consider direct current (dc) Insert Fig 5.1**Defining the direction of conventional flow for**single-source dc circuits.**Defining the polarity resulting from a conventional current**I through a resistive element.**Series Resistors**The 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).**Total Series Resistance**• The total resistance of a series circuit is equal to the sum of the resistances of each individual series resistor**Using an ohmmeter to measure the total resistance of a**series circuit.**Two series combinations of the same elements with the same**total resistance.**Series Resistors**• When series resistors have the same value, • Where N = the number of resistors in the string. • The total series resistance is found by multiplying the value of the same resistor times the number of resistors**Resistors in Series**• A series circuit provides only one path for current between two points so that the current is the same through each series resistor**Current in a Series Circuit**• The current is the same through all points in a series circuit • The current through each resistor in a series circuit is the same as the current through all the other resistors that are in series with it • Current entering any point in a series circuit is the same as the current leaving that point**Current entering any point in a series circuit is the same**as the current leaving that point.**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**Ohm’s Law in Series Circuits**• Current through one of the series resistors is the same as the current through each of the other resistors and is the total current • If you know the total voltage and the total resistance, you can determine the total current by using: • IT = VT/RT**Ohm’s Law in Series Circuits**• Current through one of the series resistors is the same as the current through each of the other resistors and is the total current • If you know the voltage drop across one of the series resistors, you can determine the current by using: I = VR/R**Notation**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.**Notation**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).**Inserting the polarities across a resistor as determined by**the direction of the current**Ohm’s Law in Series Circuits**• If you know the total current, you can find the voltage drop across any of the series resistors by using: VR = ITR • The polarity of a voltage drop across a resistor is positive at the end of the resistor that is closest to the positive terminal of the voltage source • The resistor current is in a direction from the positive end of the resistor to the negative end**Using voltmeters to measure the voltages across the**resistors**Voltage Sources in Series**• When two or more voltage sources are in series, the total voltage is equal to the the algebraic sum (including polarities of the sources) of the individual source voltages**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.**Kirchhoff’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.**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.