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. v1 v2 + – v3
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 i1 i2 i3

4. Calculate the value of v, i and power dissipated in each resistor.
vc is a rise in the direction of the current in the resistor.
Vc = -1*20 = -20V
P20Ω = i2R = 12*20
= 20 W
Id in the 25Ω resistor is in the direction of the voltage rise across the resistor.
id = -50/25=-2A
P25Ω = v2/R
= 502/25 = 100 W

5. Sum the current at each node
Node a:
i1 + i4 - i2 - i5 = 0
Node b:
i2 + i3 – i1 - ib - ia= 0
Node c:
ib – i3 – i4 - ic = 0
Node d:
i5 + ia + ic = 0
Note: no connection dot ● in the centre of the diagram

6. Sum the voltage around each designated path in the circuit
Path a
-v1 + v2 + v4 – vb – v3 = 0
Path b
-va + v3 + v5 = 0
Path c
vb – v4 – vc – v6 – v5 = 0
Path d
-va – v1 + v2 - vc + v7 – vd = 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 =R1+R2+R3+R4
Resistors in parallel:
1/Rtotal = 1/R1 +1/R2 +1/R3 +1/R4
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.
Is = Ir = Id = Ii = Ispk = Iu = If

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
12 parallel with (10Ω+14Ω)
Product over sum rule: 12*24/(12+24) = 8Ω
2, 6, and 8Ω connected in series
2+6+8 = 16Ω

11. Circuit Analysis: Example 2
18 parallel with (3+6): 18*9/(18+9) = 6
is = 120/(4+6) = 12 A
120v = V4Ω +Vxy
V4Ω = Is*R(4Ω) = 12*4 = 48 V
Vxy = = 72 V
i1 = Vxy/18 = 72/18 = 4 A
i2 = Vxy/(3+6) = 72/9 = 8 A
Confirm: is = i1 + i2

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
Band 2
Band 3
Tolerance %
Measured
Value
Error
1000Ω
Brown
Black
Red 5
2200Ω
3900Ω
Orange
White
4700Ω
Yellow
Violet
5600Ω
Green
Blue

18. Test Resistor Network (KVL)
Build the circuit below
Use N0 as your reference node (0V)
Test the voltages at each node using DVM
Component V1
VR1
VR2
VR3
VR4
VR5
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 # I1 I2 I3 I4 I5
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?