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Chap. 3 Simple Resistive Circuits

Chap. 3 Simple Resistive Circuits. C ontents. 3.1 Resistors in Series 3.2 Resistors in Parallel 3.3 The Voltage-Divider and Current-Divider Circuits 3.4 Voltage Division and Current Division 3.5 Measuring Voltage and Current 3.6 Measuring Resistance—The Wheatstone Bridge

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Chap. 3 Simple Resistive Circuits

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  1. Chap.3Simple ResistiveCircuits Contents 3.1 Resistors in Series 3.2 Resistors in Parallel 3.3 The Voltage-Divider and Current-Divider Circuits 3.4 Voltage Division and Current Division 3.5 Measuring Voltage and Current 3.6 Measuring Resistance—The Wheatstone Bridge 3.7 Delta-to-Wye (Pi-to-Tee) Equivalent Circuits Objectives 1. 能分辨電阻器連接之串、並聯方式，並使用其串並聯規則，求得等效電阻值。 2. 了解如何設計簡單的分壓器及分流器電路。 3. 能適時地利用分壓器及分流器來求解簡單的電路。 4. 當安培計加至電路中以測量電流時，能決定其讀值； 當伏特計加至電路中以測量電壓時，也能決定其讀值。 5. 了解如何利用惠斯登電橋來測量電阻值。 6. 了解如何適時的利用△ -Y 等效電路來求解簡單的電路。

  2. 3.1 Resistors in Series Combining Resistors in Series 串聯的電路元件(series-connected circuit elements) 承載著相同的電流。 只要利用KCL就可證明流過的電流是相同的。 KVL

  3. 3.2 Resistors in Parallel Combining Resistors in Parallel 並聯的電路元件(parallel-connected circuit elements)： 元件兩端分別接在相同的兩節點，具有相同的電壓。 注意:(a)並非元件並排就是並聯；(b)並非兩端電壓值相同就是並聯。 KCL: Ohm’s law: OR

  4. EX 3.1 Applying Series-Parallel Simplification

  5. 3.3 The Voltage-Divider andCurrent-Divider Circuits KVL & Ohm’s law load Voltage-Divider Circuit 可從一個電壓源獲得一個以上的電壓準位 負載(load): 由一個或多個電路元件所形成，它會取用電路的功率。 若RL>>R2，則不影響vo/vs的比例值。

  6. EX 3.2 Analyzing the Voltage-Divider Circuit The resistors used in the voltage-divider circuit have a tolerance of ±10%. Find the maximum and minimum value of vo.

  7. Current-Divider Circuit Current-Divider Circuit KCL & Ohm’s law EX 3.3 Analyzing a Current-Divider Circuit 分流 分流

  8. 3.4Voltage Division and CurrentDivision Voltage Division Current Division

  9. EX 3.4 Using Voltage Division & Current Division 分流 分壓

  10. 3.5Measuring Voltage and Current Ammeter (安培計):用來測量電流的儀器 和待測電路元件以串聯方式連接；理想的安培計其等效電阻值為0 Ω，如同一個短路和待測電路元件串聯，不會影響待測電路元件的電流值。 In series In parallel short circuit open circuit Voltmeter (伏特計):用來測量電壓的儀器 和待測電路元件以並聯方式連接；理想的伏特計其等效電阻值為 ，如同一個開路和待測電路元件並聯，不會影響待測電路元件的電壓值。

  11. Digital meters & Analog meters Digital Meters (數位電錶):以離散方式測量連續電壓或電流的裝置。 在某時間只取一點或稱為取樣時間來測量連續的電壓或是電流信號， 也就是將類比信號（時間是連續的）轉換成數位信號。 Analog Meters (類比電錶):以達松法表頭(d’Arsonval meter movement) 測量讀出連續電壓或電流的裝置。 表頭設計的原則是：指針偏轉的量和通過可轉線圈的電流成正比。線圈可以用電壓及電流值來描述。如商用表頭的額定值為50mV, 1 mA；則代表線圈通過1 mA 電流時，線圈兩端的電壓降為50 mV。 RA: 限制通過表頭的電流量 Rv: 限制跨於表頭線圈兩端的壓降

  12. EX 3.5 Using a d’Arsonval Ammeter 50mV, 1 mA 50  a) Determine RAfora full-scale reading of 10 mA.. b) How much resistance is added to the circuit when the 10 mA ammeter is inserted to measure current? a)  b) OR

  13. EX 3.6 Using a d’Arsonval Voltmeter 50mV, 1 mA 50  a) Determine Rvfora full-scale reading of 150 V. b) How much resistance doesthe 150 V meter insert into the circuit? a)  b) OR

  14. 3.6Measuring Resistance — The Wheatstone Bridge 高電阻所造成漏電流與分支電流量相當時，以及低電阻因熱效應(i2R)造成金屬接觸熱電電壓時，均易使測量結果不準。 Wheatstone Bridge (惠斯登電橋): 用以測量中等電阻值（1Ω 至1MΩ）的一種電路形態，包含一個直流電壓源、一個檢測器及四個電阻器，其中一個電阻器之電阻值是可變的(如圖中的R3)，檢測器通常是使用微安範圍的達松法電流計，或稱為微流計/檢流計(galvanometer)。 調整可變電阻器R3，使得微流計沒有電流流過，即 ig = 0 &

  15. 3.7 Delta-to-Wye (Pi-to-Tee) Equivalent Circuits Delta () or Pi ()interconnection Wye (Y) or Tee (T)interconnection Delta-to-Wye (-to-Y) or Pi-to-Tee (-to-T)Transformation

  16. Delta-to-Wye Transformation Delta-to-Wye (-to-Y) or Pi-to-Tee (-to-T)Transformation Proof:   Y Y  

  17. EX 3.7 Applying a Delta-to-Wye Transform

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