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Principles of Computer Engineering: Lecture 3: Kirchhoff’s Laws.

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Presentation on theme: "Principles of Computer Engineering: Lecture 3: Kirchhoff’s Laws."— Presentation transcript:

1 Principles of Computer Engineering: Lecture 3: Kirchhoff’s Laws

2 Kirchhoff’s Voltage Law (KVL)  “The algebraic sum of all voltages around any closed path in a circuit is zero” (positive for a voltage rise, negative for a voltage drop. v1v1 v2v – – – v3v3 Correct your lab manual p32

3 Kirchhoff’s Current Law (KCL)  “The algebraic sum of all currents at any node (junction) in a circuit is zero” (positive for a current leaving a node, negative for coming a node) or restate as  “ The sum of currents flowing into a junction is equal to the sum of currents flowing out a junction i1i1 i2i2 i3i3

4 Calculate the value of v, i and power dissipated in each resistor. v c is a rise in the direction of the current in the resistor. V c = -1*20 = -20V P 20Ω = i 2 R = 1 2 *20 = 20 W I d in the 25Ω resistor is in the direction of the voltage rise across the resistor. i d = -50/25=-2A P 25Ω = v 2 /R = 50 2 /25 = 100 W

5 Sum the current at each node Note: no connection dot ● in the centre of the diagram Node a: i 1 + i 4 - i 2 - i 5 = 0 Node b: i 2 + i 3 – i 1 - i b - i a = 0 Node c: i b – i 3 – i 4 - i c = 0 Node d: i 5 + i a + i c = 0

6 Sum the voltage around each designated path in the circuit Path a -v 1 + v 2 + v 4 – v b – v 3 = 0 Path b -v a + v 3 + v 5 = 0 Path c v b – v 4 – v c – v 6 – v 5 = 0 Path d -v a – v 1 + v 2 - v c + v 7 – v d = 0

7 Resistors Components which resist or reduce the flow of current in a circuit are called resistances, the unit of resistance is the ohm (Ω). They are used in circuits to control or limit the amount of current flow in a wire,and to be a current-to voltage convertor. Resistors in series: R total =R 1 +R 2 +R 3 +R 4 Resistors in parallel: 1/R total = 1/R 1 +1/R 2 +1/R 3 +1/R 4 The total resistor of a parallel resistor network is always dominated by, and is less than, the smallest resistor.

8 All components connected in series have the same current flowing through them. I s = I r = I d = I i = I spk = I u = I f

9 All components connected in parallel have the same voltage across them

10 Circuit Analysis: Example 1  Combining series and parallel resistors accordingly to simplify circuits and determine equivalent resistances

11 Circuit Analysis: Example 2

12 Circuit Analysis: Example 3

13 Summary  Introduced Kirchoff’s Laws  Resistor network simplification  Simple circuit analysis

14 Principles of Computer Engineering: Labs Experiment 3: Kirchoff’s Laws

15 Overview  Build a simple resistor network and measure the voltages at each node  Use results to verify Kirchoff’s Voltage Law  Calculate the currents through each node and compare to Kirchoff’s Current Law

16 Resistors Colour Codes

17 Resistor Colour Codes  Identify the following resistors based on their colour codes {1kΩ, 2.2kΩ, 3.9kΩ, 4.7kΩ & 5.6kΩ}  Measure them and calculate actual error %  Populate table with expected colour for each value Resistor Value Colour Band 1 Colour Band 2 Colour Band 3 Tolerance % Measured Value Error % 1000Ω BrownBlackRed5 2200Ω Red Ω OrangeRed5 4700Ω YellowVioletRed5 5600Ω GreenBlueRed5

18 Test Resistor Network (KVL)  Build the circuit below  Use N0 as your reference node (0V)  Test the voltages at each node using DVM ComponentV1VR1VR2VR3VR4VR5 Voltage[V]±1%

19 Check each of three loops that KVL is preserved Loop 1 =>– V1 + VR1 + VR2 = 0 or equivalently V1 = VR1 + VR2 Loop 2 =>– VR2 + VR3 + VR4 = 0 or equivalently VR2 = VR3 + VR4 Loop 3 =>– VR4 + VR5 = 0 or equivalently VR4 = VR5

20 Test Resistor Network (KCL)  Calculate the currents passing in each loop from voltages measured previously.  DO NOT MEASURE CURRENTS DIRECTLY  Verify KCL at each node within error margins

21 Verify KCL at the two nodes (N2 and N3) Current #I1I2I3I4I5 Current [A] ±__% Node 2 =>– I1 + I2 + I3 = 0 or equivalently I1 = I2 + I3 Node 3 =>– I3 + I4 + I5 = 0 or equivalently I3 = I4 + I5

22 Summary  Build resistor network and test  Measure voltages at each node  Calculate currents passing through each node  Verify both KVL and KCL  Consider sources of errors in this experiment  Put all your results and notes into your logbook!  Any questions?


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