Engr228 - Chapter 3, Nilsson 11E 1

Chapter 3Simple Resistive Circuits

Engr228

Circuit Analysis

Dr Curtis Nelson

Chapter 3 Objectives

• Be able to recognize resistors connected in series and in parallel and use the rules for combining them;

• Know how to analyze voltage-divider and current-divider circuits;

• Be able to recognize when voltage or current division can be used to solve a circuit;

• Be able to use ammeters, voltmeters, and ohmmeters correctly.

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Series Connections

• Elements connected head-to-tail and carrying the same current are said to be connected in series.

Resistors in Series

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Voltage Division

Resistors in series “share” the voltage applied to them.

Voltage Divider Example

10V

4K

6K

V1

Calculate V1 using the voltage divider equation.

V1 = 4.00V

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Textbook Problem 3.12 (Nilsson 10th)

Find the voltage v0 and the power dissipated in both resistors.

v0 = 66VPR1 = 1.88WPR2 = 1.32W

Parallel Connections

• Elements in a circuit connected head-to-head and tail-to-tail have a common voltage across them and are said to be connected in parallel.

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Resistors in Parallel

Two Resistors in Parallel

Connecting resistors in parallel makes the equivalent resistance smaller. Always.

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Current Division

Resistors in parallel “share” the current through them.

Current Divider Example

4K2K1mA

Calculate the current in the two resistors below using the current divider equation.

i2K = 0.667mAi4K = 0.333mA

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Textbook Problem 3.2d (Nilsson 11th)

Compute the equivalent resistance seen by the 30 mA source.

Answer: R = 120Ω

Textbook Problem 3.19 (Nilsson 11th)

For the current divider shown below, calculate i0 and v0.

Answer: i0 = 0.16A and v0 = 16V

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Measuring Voltage and Current

• An ammeter is an instrument designed to measure current; it is placed in series with the circuit element whose current is being measured.

• A voltmeter is an instrument designed to measure voltage; it is placed in parallel with the element whose voltage is being measured.

Measuring Resistance

• An ohmmeter is an instrument designed to measure resistance; it is placed in parallel with the resistive circuit whose resistance is being measured. Note that accurate measurements of resistance require that the resistive circuit have no energy present (no voltage or current).

• Often, one instrument – called a multimeter – is used to measure all three parameters, but not all at once.

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Fluke Multimeters

Measuring Voltage, Current, and Resistance

• An ideal meter has no effect on the circuit variable being measured.

• That means when an ideal ammeter is placed in series to measure the current through an element, it should have an equivalent resistance of 0 Ω.

• That means when an ideal voltmeter is placed in parallel to measure the voltage across an element, it should have an equivalent resistance of ∞ Ω.

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Textbook Problem 3.39 (Nilsson 11th)

An ammeter with an internal resistance of 0.1Ω is used in the circuit below. Find the percentage error in the measured value using the following formula:

%Error = [(Measured value – True value)/True value]*100%

Answer: % error = -0.347%

Example: Circuit Simplifying

Find i and the power supplied by the 80V source.

Answer: i = 3 A and p = 240 W supplied

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Chapter 3 Summary

• Showed how to recognize resistors connected in series and in parallel and how to combine them;

• Explained the use of voltage and current division;• Explained how to analyze voltage-divider and current-divider

circuits;• Showed how to use ammeters, voltmeters, and ohmmeters

correctly.