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Chapter 5 Series Circuits

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**Objectives Identify a series circuit**

Determine the current in a series circuit Determine total series resistance Apply Ohm’s law in series circuits Determine the total effect of voltage sources in series

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**Objectives Apply Kirchhoff’s voltage law**

Use a series circuit as a voltage divider Determine power in a series circuit Determine and identify ground in a circuit

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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.

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**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.

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**Total Series Resistance**

The total resistance of a series circuit is equal to the sum of the resistances of each individual series resistor.

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**Series Resistance Formula**

For any number of individual resistors connected in series, the total resistance is the sum of each of the individual values. RT = R1 + R2 + R Rn

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**Ohm’s Law in Series Circuits**

Current through one of the series resistor is the same as the current through each of the other resistors and is the total current. Itotal = IR1 = IR2 = …. If you know the total voltage and the total resistance, you can determine the total current by using: IT = VT/RT If you know the voltage drop across one of the series resistors, you can determine the current by using: I = VR/R

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**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

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**Ohm’s Law in Series Circuits**

An open in a series circuit prevents current; and, there is zero voltage drop across each series resistor. The total voltage appears across the points between which there is an open.

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Series Resistors

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**All circuits have three common attributes. These are:**

Series circuits All circuits have three common attributes. These are: 1. A source of voltage. 2. A load. 3. A complete path. A series circuit is one that has only one current path.

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**Series circuit rule for current:**

Because there is only one path, the current everywhere is the same. 2.0 mA For example, the reading on the first ammeter is 2.0 mA, What do the other meters read? 2.0 mA 2.0 mA 2.0 mA

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**Series circuits The total resistance of resistors in series is**

the sum of the individual resistors. For example, the resistors in a series circuit are 680 W, 1.5 kW, and 2.2 kW. What is the total resistance? 4.38 kW

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Series circuits Tabulating current, resistance, voltage and power is a useful way to summarize parameters in a series circuit. Continuing with the previous example, complete the parameters listed in the Table. I1= R1= 0.68 kW V1= P1= I2= R2= 1.50 kW V2= P2= I3= R3= 2.20 kW V3= P3= IT= RT= 4.38 kW VS= 12 V PT= 2.74 mA 1.86 V 5.1 mW 2.74 mA 4.11 V 11.3 mW 2.74 mA 6.03 V 16.5 mW 2.74 mA 32.9 mW

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**Voltage sources in series**

Voltage sources in series add algebraically. For example, the total voltage of the sources shown is 27 V What is the total voltage if one battery is reversed? Question: 9 V

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**Voltage Sources in Series**

A voltage source is an energy source that provides a constant voltage to a load. Batteries and electronic power supplied are practical examples of dc voltage sources.

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**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.

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**Kirchhoff’s Voltage Law**

The sum of all the voltage drops around a single closed loop in a circuit is equal to the total source voltage in that loop. VS = V1 + V2 + V3 + … + Vn

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**Another Way to state Kirchhoff’s Voltage Law**

The algebraic sum of all voltages (both sources and drops) around a closed path is zero. VS - V1 - V2 - V3 = 0

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Voltage Dividers Since each resistor has the same current, the voltage drops are proportional to the resistance values.

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**Voltage-Divider Formula**

The voltage drop across any resistor or combination of resistors in a series circuit is equal to the ratio of that resistance value to the total resistance, multiplied by the source voltage. Vx = (Rx/RT)VS

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**Potentiometer as an Adjustable Voltage Divider**

The potentiometer shown below is equivalent to a two-resistor voltage divider that can be manually adjusted. The two resistors are between terminals 1 and 3, and 2 and 3.

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**Power in a Series Circuit**

The total amount of power in a series resistive circuit is equal to the sum of the powers in each resistor in series. PT = P1 + P2 + P Pn

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Power in a Resistor The amount of power in a resistor is important because the power rating of the resistor must be high enough to handle the expected power in the circuit.

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**Circuit Ground Voltage is relative.**

The voltage at one point in a circuit is always measured relative to another point. This reference point is usually the ground point.

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**Measuring Voltages with Respect to Ground**

When voltages are measured with respect to ground in a circuit, one meter lead is connected to the circuit ground, and the other to the point at which the voltage is to be measured.

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**Measuring Voltage Across an Ungrounded Resistor**

Voltage can normally (as long as the meter is isolated from the power line ground) be measured across a resistor even though neither side of the resistor is connected to circuit ground. The reading will be the voltage drop across the resistor.

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**Open Circuit The most common failure in a series circuit is an open.**

When an open occurs in a series circuit, all of the source voltage appears across the open.

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Short Circuit When there is a short, a portion of the series resistance is bypassed, thus reducing the total resistance. A short in a series circuit results in more current than normal.

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**A Short in a Series Circuit**

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**Summary Current is the same at all points in a series circuit.**

The total resistance between any two points in a series circuit is equal to the sum of all resistors connected in series between those two points. Voltage sources in series add algebraically. Kirchhoff’s voltage law (KVL): The sum of all the voltage drops around a single closed loop in a circuit is equal to the total source voltage in that loop.

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Summary Alternative KVL: The algebraic sum of all voltages (both sources and drops) around a closed path is zero. The voltage drops in a circuit are always opposite in polarity to the total source voltage. Conventional current is out of the positive side of a source and into the negative side. Conventional current is into the positive side of each resistor and out of the more negative side.

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Summary A voltage drop is considered to be from a more positive voltage to a more negative voltage. A voltage divider is so named because the voltage drop across any resistor in the series circuit is divided down from the total voltage by an amount proportional to that resistance value in relation to the total resistance. A potentiometer can be used as an adjustable voltage divider.

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Summary The total power in a resistive circuit is the sum of all the individual power of the resistors making up the series circuit. Ground is zero volts with respect to all points referenced to it in the circuit. The voltage across an open series element equals the source voltage. A short in a series circuit causes more current than normal.

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