EE215 FUNDAMENTALS OF ELECTRICAL ENGINEERING

Transcription

1 EE215 FUNDAMENTALS OF ELECTRICAL ENGINEERING Tai-Chang Chen University of Washington, Bothell Spring 2010 EE

2 WEEK 2 SIMPLE RESISTIVE CIRCUITS April 9 th, 2010 TC Chen UWB 2010 EE

3 QUESTIONS TO ANSWER Kirchoff s Laws What are KVL and KCL? How to apply both laws on an electric circuit? Simplifying Resistive Circuits How to simplify circuits using resistors in series and /or in parallel? Voltage Division and Current Division How to develop more than one voltage level and current level using the techniques? How to apply the techniques to measure circuit variables and parameters? EE215 3 TC Chen UWB

4 KIRCHHOFF S LAWS a 10 b 120V A 50 B 6A Def.: Node a point where 2 or more circuit elements meet. A point of connection. c Def.: Loop or Closed Path path that follows circuit elements from node to node until returning to the starting point. EE215 TC Chen UWB

5 KIRCHHOFF S CURRENT LAW (KCL) A node is just a point - it can't store charge. So charge flowing in to a node must flow out of it. Flow of charge is just current, of course. A clever way to say this is: (We could also say the sum of currents flowing out of a node is zero. But we say "into" because a guy named Kirchhoff said into, and got his name on the saying as) EE215 5 TC Chen UWB

6 KIRCHHOFF S CURRENT LAW (KCL) i j Node 0 Examples: (a) (b) EE215 TC Chen UWB

7 KIRCHHOFF S VOLTAGE LAW (KVL) The sum of voltages around a closed path is zero. vk Loop Examples: (a) 0 (b) What is v 0? EE215 TC Chen UWB

8 KIRCHHOFF S VOLTAGE LAW (KVL) To deal correctly with polarity: IT DOES NOT MATTER WHICH CHOICE YOU MAKE AS LONG AS YOU APPLY IT CONSISTENTLY. EE215 8 TC Chen UWB

9 MORE ON THE LAST EXAMPLE 4V 5V v 0 3V 2V i* R 0 = 1 Going around circuit loop counterclockwise: Alternatively, going around the circuit loop clockwise: EE215 TC Chen UWB

10 BACK TO PREVIOUS EXAMPLE Example 2.8: a 10 i 0 b 120V A 50 B 6A i 1 KCL at b: (1) KVL at cabc: (2) With Ohm s Law: (2 ) Two equations, two unknowns (i 0 and i 1 ): c EE215 TC Chen UWB

11 DEVELOPED / DISSIPATED POWER Power at voltage source: Power at current source: Power at R 0 = 10 resistor: Power at R 1 = 50 resistor: EE TC Chen UWB

12 RESISTORS IN SERIES We often find resistors in series. (Connected to the same node at one end, and different nodes at opposite ends. Nothing can be connected to the middle node.) The same current flows through both resistors (a basic test for series connection). EE TC Chen UWB

13 RESISTORS IN SERIES There are two things that are easy to do when you see a two (or more) resistors in series. They are: i v 1 R 1 v s - - v 2 R 2 Note that you can't do both at the same time! If you combine resistors, the node between them goes away! - EE215 TC Chen UWB

14 RESISTORS IN SERIES Let's do replacement first. We want to find R eq such that current i is unchanged, for a given voltage v s. From KVL on the original circuit i v s - R eq EE215 TC Chen UWB

15 RESISTORS IN SERIES Example: v s i s R 1 R 2 R 3 R 4 i 1 i 2 i 3 i 4 i 5 i 9 i 8 i 7 i 6 R 5 KCL: R 9 R 8 R 7 R 6 KVL: The 9 resistors can be replaced by a single resistor: EE215 TC Chen UWB

16 RESISTORS IN PARALLEL We often find resistors in parallel - connected to same node at both ends. Voltage across resistors is the same. Can we replace? i s i 1 i 2 v s R 1 R 2 - EE215 TC Chen UWB

17 RESISTORS IN PARALLEL Example: v i s i 1 R i 2 i 3 i s 1 R 2 R 3 4 R 4 KCL: Ohm s Law: So: Substitute: The 4 resistors can be replaced by a single resistor: EE215 TC Chen UWB

18 RESISTORS IN PARALLEL Special case 2 resistors: Special case 3 resistors: Is this formula correct? Correct formula: EE TC Chen UWB

19 VOLTAGE DIVIDER Often, developing more than one voltage level from a single voltage supply is useful. Output voltage EE TC Chen UWB

20 CURRENT DIVIDER Similarly to the voltage divider, we can develop various currents from a single current source. Or in terms of conductance: EE TC Chen UWB

21 VOLTAGE DIVIDER (2) What happens under load? v s i R 1 R 2 v o R L EE215 TC Chen UWB

22 MEASURING VOLTAGE AND CURRENT Def.: Ammeter instrument to measure current. Ideally, EE TC Chen UWB

23 AMMETER Example: Ammeter with range limit 1mA at 50mV Want full-scale reading of 100mA (expand range 100x) Internal resistance of ammeter We want 50mV at 100mA total current i A A R p i p EE215 TC Chen UWB

24 MEASURING VOLTAGE AND CURRENT Def.: Voltmeter instrument to measure voltage. Ideally, EE TC Chen UWB

25 MEASURING VOLTAGE AND CURRENT The instrument should be set to its highest range before being connected into the circuit. For the greatest measurement accuracy, the best range to use is the one that gives the largest deflection not exceeding full scale. EE TC Chen UWB

26 MEASURING RESISTANCE THE WHEATSTONE BRIDGE R 1, R 2 known R 3 known, variable R x unknown Procedure: EE TC Chen UWB

27 MEASURING RESISTANCE THE WHEATSTONE BRIDGE (2) Typically, a set of resistors R 1, R 2 with decimal ratio is provided: 1m, 10m, 1k v R 1 A R 3 i g R 2 R x EE215 TC Chen UWB