1. ECE 3710 E: Circuits and Electronics Jeff Dugger Lecture 4: 08/31/00

2. Voltage Sources + - Vs Provide potential to generate current I V Vs Ideal Voltage Source Provides Voltage Independent of Current Current determined by Circuit

3. Current Sources Is I V Provides Current Independent of Voltage Ideal Current Source Voltage is determined by the Circuit

4. Ohm’s Law and Resistance + - V IR V = I R I = V R 1 I V OR Units: Ohms ( ) = Volts / Amp (V/A) R 1

5. I = V G Ohm’s Law and Conductance + - V I V = I R I V OR Units: Siemens ( S ) = Amps / Volt (A/V) R 1 = G G

6. Series Resistance R1R1 VsVs R2R2 R3R3 I V1V1 V2V2 V3V3 -V s + V 1 + V 2 + V 3 = 0 V s = V 1 + V 2 + V 3 Apply KVL: V s = R 1 I + R 2 I + R 3 I Apply Ohm’s Law: = (R 1 + R 2 + R 3 ) I Define Equivalent Resistance: R eq = R 1 + R 2 + R 3 V s = R eq I

7. Voltage Divider I R1R1 VsVs R2R2 V1V1 V2V2 V 2 = R 2 IApply Ohm’s Law: Use Equivalent Resistance to find I: I = V s R 1 + R 2 1 Substitute: V 2 = V s R 1 + R 2 R2R2

8. Parallel Resistance V I s = G 1 V + G 2 V + G 3 V Apply Ohm’s Law: = (G 1 + G 2 + G 3 ) V Define Equivalent Conductance: G eq = G 1 + G 2 + G 3 I s = G eq V G 1 = G 2 = G 3 = R1R1 1 R2R2 1 R3R3 1 R1R1 R2R2 R3R3 I1I1 I2I2 I3I3 Apply KCL:I s = I 1 + I 2 + I 3 IsIs

9. Parallel Resistance R1R1 R2R2 R3R3 I1I1 I2I2 I3I3 I s = I 1 + I 2 + I 3 Apply KCL: Or, Define Equivalent Resistance: G 1 = G 2 = G 3 = V = R eq I s R1R1 1 R2R2 1 R3R3 1 R eq = G eq 1 = 1 / R 1 + 1 / R 2 + 1 / R 3 1 V IsIs

10. Current Divider R1R1 R2R2 I1I1 I2I2 I 2 = G 2 VApply Ohm’s Law: Use Equivalent Conductance to find V: V = I s G 1 + G 2 1 Substitute: I 2 = I s G 1 + G 2 G2G2 V IsIs

11. Current Divider R1R1 R2R2 I1I1 I2I2 I 2 = G 2 VApply Ohm’s Law: Use Equivalent Conductance to find V: V = I s G 1 + G 2 1 Substitute: I 2 = I s R 1 + R 2 R1R1 V IsIs Or, in terms or Resistance:

12. Series-Parallel Circuit VsVs R2R2 I1I1 V1V1 V3V3 R3R3 R1R1 I2I2 I3I3

13. VsVs R2R2 I1I1 V1V1 V3V3 R3R3 R1R1 I2I2 I3I3

14. Circuit Analysis Example VsVs R1R1 I R3R3 R2R2 I2I2 R5R5 R4R4 V

15. RaRa I V Series Combination: R a = R 1 + R 2 VsVs R3R3 I2I2 R5R5 R4R4

16. Circuit Analysis Example I RbRb V Parallel Combination: R b = R 4 || R 5 VsVs R3R3 I2I2 RaRa

17. Circuit Analysis Example I V RbRb VsVs R3R3 RaRa I2I2

18. I V KCL at this node I s = G a V + G b (V - V s ) = (G a + G b ) V - G b V s RbRb VsVs R3R3 RaRa IsIs V = G a + G b GbGb V s + G a + G b 1 IsIs

19. Circuit Analysis Example I V KCL at this node I s = G a V + G b (V - V s ) = (G a + G b ) V - G b V s RbRb VsVs R3R3 RaRa IsIs V = R a + R b RaRa V s + R a || R b I s

20. Open and Short Circuits “Open Circuit” “Short Circuit” R very large R very small R = I V R = 0 I V Any currentNo voltage No current Any voltage