Principles of Computer Engineering
Lecture 2: Introduction to Circuit Theory
Charge, Voltage & Current
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Electric Charge, e = 1.6 x 10-19 Coulombs (one electron)
The separation of charge gives rise to electric force, voltage (also
called Potential Difference)
The flow of charge gives rise to electric current
Voltage = Rate of change of Energy per unit charge (Coulomb)
1 V = 1 Joule/coulomb
Current = Rate of change of Charge per unit time (second)
1 A = 1 coulomb/second
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v = voltage (Volts)
E = Energy or w = work (Joules)
q = charge (Coulombs)
t = time (seconds)
Both voltage and current have direction or polarity
Passive Sign Convention
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“Basic Ideal Circuit Element”
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‘Basic’ → cannot be reduced
‘Ideal’ → non-realisable
Passive Sign Convention
Current is considered to be the flow of ‘positive’
charge. [In reality negative electrons flow].
(a) For an element which is a ‘consumer’, current
flows into the positive terminal to negative. P is
positive.
(b) For a generator (power supply), conventions
states that the power produced, P, is negative.
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Power and Energy
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1 Watt = 1 Joule per second.
Convention: current flowing in the opposite direction
to the flow of electrons.
1 A =1000 mA = 1,000,000 μA
1 μA = 10-3 mA = 10-6 A
1mA = 10-3 A
Independent Voltage & Current Sources
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An independent voltage
source (a) can maintain the
fixed voltage independent of
the load
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An independent current
source (b) must maintain its
specific current flow at all
times
Valid Circuits?
Ohm’s Law
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Resistance is the capacity of materials to impede
(obstruct, block) the flow of electric current.
Ohm’s Law: v = iR
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v : [Volts]
i : [Amps]
R : [Ohms or ‘Ω’]
Power measured in Watts (W)
v v
2
P  vi  (iR )i  i R  v  
R R
2
Combining Series Resistors
vs  is R1  is R2  is R3  is R4  is R5  is R6  is R7
vs  is ( R1  R2  R3  R4  R5  R6  R7 )
vs
 Req  R1  R2  R3  R4  R5  R6  R7
is
Combining Parallel Resistors
vs  i1 R1  i2 R2  i3 R3  i4 R4
is  i1  i2  i3  i4
1
vs vs vs vs
1
1
1 
is  
 
 vs  
  
R1 R2 R3 R4
 R1 R2 R3 R4 
is
1
1
1
1
1
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 
 
vs Req R1 R2 R3 R4
Voltage Divider Circuit
vs  i ( R1  R2 )
v1  iR1 v2  iR2
vs
v1


R1 R1  R2
 R1 

 v1  vs 
 R1  R2 
 R2 

 v2  vs 
 R1  R2 
Current Divider Circuit
v  i1 R1  i2 R2
v  is Requiv
 R1 R2 

i1 R1  is 
 R1  R2 
R1 R2
Requiv 
R1  R2
 R2 

i1  is 
 R1  R2 
 R1 

& i2  is 
 R1  R2 
Summary
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Introduced simple circuit theory
Concepts of charge, voltage and current
Passive sign convention, flow of conventional current
Concept of power dissipation
Potential and current dividers
Questions?
Principles of Computer Engineering:
Experiment 2: Ohm’s Law & Power
Overview
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Introduction to Ohm’s Law and Power dissipation
Read resistor codes and tolerance values
Build simple to test potential and current dividers
Appreciate component tolerances and measurement errors
Resistors Colour Codes
Procedure 1: Ohm’s Law & Power
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Build circuit pictured
Measure current for different
values of resistor
Calculate power dissipation
Draw graph to show power vs.
resistance
A
Procedure 2: Voltage Divider
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Build circuit pictured
Measure voltage for different
values of resistance R2
Calculate theoretical value of V2
across R2
𝑉2 =
𝑅2
𝑉𝑠
𝑅1 +𝑅2
=10*1/2 = 5v
and 7.5, 9, 9.5V.
 Compare with measured values
for four different R2
Lab manual P30 table 2
R1 [] ±___%
R2 [] ±___%
set
VR2 [V] ±___%
measurements
Theoretical VR2 [V]
𝑉𝑅2 = 𝑉𝑠
1000
1000
5
1000
3000
7.5
1000
9000
9
1000
19000
9.5
𝑅2
𝑅1 + 𝑅2
Procedure 3: Current Divider
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Build circuit pictured
Measure current for different
values of resistance R2
Calculate theoretical value of
I2 through R2
Compare with measured
values for four different R2
NB: Must calculate equivalent
resistance and source current
A
Lab manual P31 table 2
R1 [] ±__%
R2 [] ±__%
set
1000
1000
1000
3000
1000
9000
1000
19000
Rtotal [] ±__%
R1||R2 =
R1*R2/(R1+R2)
Is [mA] ±__% IR2 [mA] ±__% Theory IR2 [mA]
Is = 10v/Rtotal measurements 𝐼𝑅2
𝑅1
= 𝐼𝑠
𝑅1 + 𝑅2
R1 [] ±__%
R2 [] ±__%
set
Rtotal [] ±__%
R1||R2 =
R1*R2/(R1+R2)
Is [mA] ±__% IR2 [mA] ±__% Theory IR2 [mA]
Is = 10v/Rtotal measurements 𝐼𝑅2
𝑅1
= 𝐼𝑠
𝑅1 + 𝑅2
1000
1000
500
20
10
1000
3000
750
13.33
3.3
1000
9000
900
11.1
1.1
1000
19000
950
10.5
0.52
Summary
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Become familiar with Ohm’s Law and resistor colour codes
Build elementary circuits to determine power dissipation
Verify via practical experimentation the theory behind voltage
and current dividers
Appreciate error margins and component tolerances
Questions?