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Principles of Computer Engineering:
Lecture 3: Kirchhoff’s Laws
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.
+
v3
–
–
v2
+
+
 v1  v2  v3  0
v1
 v1  v2  v3  0
–
v1  v2  v3
Correct your lab manual p32
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
 i1  i2  i3  0
 i1  i2  i3  0
i3
i1  i2  i3
Sum the current at each node
Node a:
i1 + i 4 - 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
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
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.
All components connected in series have the same current flowing through them.
Is = Ir = Id = Ii = Ispk = Iu = If
All components connected in parallel have the same
voltage across them
Circuit Analysis: Example 1

Combining series and parallel resistors accordingly to simplify
circuits and determine equivalent resistances
Circuit Analysis: Example 2
Circuit Analysis: Example 3
Summary



Introduced Kirchoff’s Laws
Resistor network simplification
Simple circuit analysis
Principles of Computer Engineering:
Labs Experiment 3: Kirchoff’s Laws
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
Resistors Colour Codes
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
%
1000Ω
Brown
Black
Red
5
2200Ω
Red
Red
Red
5
3900Ω
Orange
White
Red
5
4700Ω
Yellow
Violet
Red
5
5600Ω
Green
Blue
Red
5
Measured
Value
Error
%
Test Resistor Network (KVL)



Build the circuit below
Use N0 as your reference node (0V)
Test the voltages at each node using DVM
Component
Voltage[V]±1%
V1
VR1
VR2
VR3
VR4
VR5
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
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
Verify KCL at the two nodes (N2 and N3)
Current #
Current [A]
±__%
I1
I2
I3
I4
I5
Node 2 =>
– I1 + I2 + I3 = 0
or equivalently
I1 = I2 + I3
Node 3 =>
– I3 + I4 + I5 = 0
or equivalently
I3 = I4 + I5
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?