Download presentation

Presentation is loading. Please wait.

Published byHalie Parsley Modified about 1 year ago

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?

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google