1. Engineering Fundamentals Session 4 (3 hours)

2. Resistance Amount of current flows in an electric circuit depends on the resistance of the material through which it travels I=V/R A resistor is a device which provides resistance in an electrical circuit R=V/I SI unit is ohm, written as  1  =1 VA -1

3. An electric circuit is a connection of sources and loads in any way which allow charge to flow. e.g. a simple circuit with a battery and a light bulb Relationship between current direction and voltage polarity V=____ V=_____ I + 10V -

4. Consider the following circuit: –What is the voltage V R through the 5  resistor, and its polarities? –What is the current I, and its direction? +V-+V- 10 +V-+V- 5 V R 5 

5. Measuring resistance Voltmeter-ammeter method R=V/I Multimeter What is the resistance of your body? A V

6. An open circuit occurs when a conductor is broken between the points under test. A short circuit occurs when a low resistance conductor such as a wire is connected R=____

7. Ohm ’ s Law Voltage across two ends of a resistor is directly proportional to the current flowing through it. I V V-I graph for a resistor that obeys Ohm’s law V=IR I + V -

8. Resistors in series A series circuit has only one path for current to flow –Example: – Same current through each resistor I = I 1 = I 2 R2R2 R1R1 + V 1 -+ V 2 - I + V - I1I1 I2I2

9. –Applying Ohm ’ s law to each resistor, V 1 = IR 1, V 2 = IR 2 –Voltage of the source equals sum of V 1 and V 2 V = V 1 + V 2 = IR 1 + IR 2 = I (R 1 + R 2 ) = I R –Equivalent resistance R = R 1 + R 2 –In general R = R 1 + R 2 + R 3 + + R n R1R1 R2R2 R3R3 RnRn

10. Example: –What is the equivalent resistance? –What are the currents I 1, I 2 through the resistors? –What are their directions? –What is the voltage across each resistor? Indicate the relative voltage polarities (+,-) 12V 2  4  V 1 V2V2 I I1I1 I2I2

11. Solution: –Equivalent resistance = 2  + 4  = 6  –Current I = V/R = 12V/6  =2A 12V 2  4  12V 6  + 12V - 2  4  I I1I1 I2I2

12. Solution: –V = IR Voltage across 2  resistor = 2A*2  = 4V Voltage across 4  resistor = 2A*4  = 8V + 12V - 2  4  + 4V -+ 8V - I I1I1 I2I2

13. Consider the following circuit: –What are the voltages V 1, V 2, V 3, and V 4, and their corresponding polarities 極性 ? –What is the current? and its direction? +V-+V- 10 V 1 5  V 3 V 2 V 4 5 

14. Consider the following circuit: –What are the voltages V 1, V 2, V 3, and V 4, and their corresponding polarities? –What is the current, and its direction? +V-+V- 10 V 1 5  V 3 V 2 V 4 5 

15. Resistors in Parallel A parallel circuit has more than one path for current to flow –Example: – Same voltage across each resistor V = V 1 = V 2 R2R2 R1R1 + V 2 - + V 1 - I2I2 I1I1 + V - I

16. –Applying Ohm ’ s law to each resistor, V = I 1 R 1, V = I 2 R 2 –Sum of current in branches equal to current I I = I 1 + I 2 = V/R 1 +V/R 2 = V (1/R 1 +1/R 2 ) = V 1/R –Equivalent resistance 1/R = 1/R 1 +1/R 2 –In general 1/R = 1/R 1 +1/R 2 +1/R 3 + +1/R n R1R1 R2R2 R3R3 RnRn......

17. Consider the following with R 1 > R 2 What can be said about the equivalent resistance R ? (a) R > R 1 (b) R 2 < R < R 1 (c) R < R 2 R1R1 R2R2 R

18. Example: –What is the equivalent resistance? –What are the currents through the resistors and their directions? –What is the total current? 12V 2  4 

19. Solution: –Equivalent resistance: 1/R = 1/R 1 +1/R 2 = 1/2 + 1/4 = 3/4 R = 4/3  –Same voltage across each resistor = 12V I 1 =current through 2  =V/R 1 =12V/2  =6A I 2 =current through 4  =V/R 2 =12V/4  =3A –Total current I = I 1 + I 2 = 6A + 3A = 9A 12V 2  4  12V 4/3 4/3  I I1I1 I2I2

20. Example: –What is the equivalent resistance? –What is the supply voltage (V s )? –What are the voltages across AB (V AB ), BC (V BC )? What are the currents through the resistors (I 20 , I 30  ) ? 30  unknown voltage supply 10  20  B C A 2A +Vs-+Vs- + V AB - + V BC - I20I20 I 30 

21. Solution: –Equivalent resistance R = 22  30  unknown voltage supply 10  20  B C A 2A unknown voltage supply 10  12  B C A 2A unknown voltage supply 22  B C A 2A

22. Solution: –Supply voltage V s =IR=2A*22  =44V –Voltage across AB, V AB =2A*10  =20V Voltage across BC, V bc =V-V AB =44V-20V=24V 30  unknown voltage supply 10  20  B C A 2A unknown voltage supply 10  12  B C A 2A +Vs-+Vs- +Vs-+Vs- + V AB - + V BC - + V BC -

23. Solution: –Current through 20  resistor I 1 = V BC / 20  = 1.2A –Current through 30  resistor I 2 = V BC / 30  = 0.8A Check total current I 1 + I 2 = 1.2A + 0.8A = 2A 30  unknown voltage supply 10  20  B C A 2A I1I1 I2I2

24. Some problems to work in class: – Problem 1: What is the equivalent resistance between A and B? 33 99 99 B A 99 33 33

25. –Problem 2: What is the equivalent resistance between A and B? 88 88 BA 88 88