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Transcript

Chapter 3 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 to yield equivalent resistance; • Know how to design simple voltage-divider and currentdivider circuits; • Be able to use voltage and current division appropriately to solve simple circuits; • Be able to use ammeters, voltmeters, and ohmmeters correctly. Engr228 - Chapter 3, Nilsson 10E 1 Series Connections • Elements connected head-to-tail and carrying the same current are said to be connected in series. Resistors in Series Engr228 - Chapter 3, Nilsson 10E 2 Voltage Division Resistors in series “share” the voltage applied to them. Voltage Divider Example Calculate V1 using the voltage divider equation. 6K V1 10V 4K V1 = 4.00V Engr228 - Chapter 3, Nilsson 10E 3 Voltage Divider for N Resistors General form of N resistors connected in series: 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. Engr228 - Chapter 3, Nilsson 10E 4 Resistors in Parallel Two Resistors in Parallel Two resistors in parallel can be combined using the product/sum shortcut. Connecting resistors in parallel makes the equivalent resistance smaller. Engr228 - Chapter 3, Nilsson 10E 5 Current Division Resistors in parallel “share” the current through them. Current Divider Example Calculate the current in the two resistors below using the current divider equation. 1mA 2K 4K i2K = 0.667mA i4K = 0.333mA Engr228 - Chapter 3, Nilsson 10E 6 Textbook Problem 3.5d Nilsson 10th Compute the equivalent resistance seen by the source. Answer: R = 120Ω Textbook Problem 3.57 Hayt 7E Compute the equivalent resistance of the circuit below. Answer: R = 5.5KΩ (5500Ω) Engr228 - Chapter 3, Nilsson 10E 7 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 is used to measure all three parameters, but not all at once. Engr228 - Chapter 3, Nilsson 10E 8 Fluke Multi-meters Measuring Voltage, Current, and Resistance • An ideal meter has no effect on the circuit variable being measured. • That means when an ammeter is placed in series to measure the current through an element, it should have an equivalent resistance of 0 Ω. • That means when a voltmeter is placed in parallel to measure the voltage across an element, it should have an equivalent resistance of ∞ Ω. Engr228 - Chapter 3, Nilsson 10E 9 Textbook Problem 3.34 Nilsson 9th An ammeter with an internal resistance of 0.1Ω is used to measure i0 in the circuit shown below. Find the percentage error in the measured value using the following formula: %Error = [(Measured value – True value)/True value]*100% Answer: % error = -0.17% Example: Circuit Simplifying Find i and the power supplied by the 80V source. Answer: i = 3 A and p = 240 W supplied Engr228 - Chapter 3, Nilsson 10E 10 Example Find V1 in the circuit below: 2K 2K 10V + V1 - 4K V1 = 2K ×10V = 3.33V 2K + 4K Example Find I in the circuit below: + I Vx 4Ω 5V 1V 2Ω + - 3Vx − 5 + 4 I + 1 + 2 I + 3Vx = 0, (Vx = 4 I ) − 5 + 4 I + 1 + 2 I + 12 I = 0 18 I = 4 I = 0.222 A Engr228 - Chapter 3, Nilsson 10E 11 Example Find the voltage, current, and power associated with each element in the circuit below: 120A Answer: 1/30Ω 30A 1/15Ω v par = 2 V , i1 = 60 A, i2 = 30 A PR1 = 120W , PR 2 = 60 W P120 A = −240W , P30 A = 60 W Chapter 3 Summary • Showed how to recognize resistors connected in series and in parallel, and how to use the rules for combining them to yield equivalent resistance; • Explained how to design simple voltage-divider and currentdivider circuits; • Explained the use of voltage and current division; • Showed how to use ammeters, voltmeters, and ohmmeters correctly. Engr228 - Chapter 3, Nilsson 10E 12