LEVEL 3 E&E ENGINEERING - DC CIRCUITS INFORMATION AND EQUATIONS
Voltage, Current, Resistance and Power
Subject
Force between charged
particles (Coulombs Law)
Equation
F=
k e q1 q 2
r2
Variables and Units
F = [attractive or repulsive] force in
Newtons (N)
*1 Ke = Coulomb’s constant (Nm2C-2)
Current
Energy
I=
Q
t
E = QV
*2 q = particle charge in Coulombs (C)
r = distance between particles (m)
I = Current in Amps (A)
Q = [total] charge in Coulombs (C)
Resistance
Conductance
R= ρ
L
A
A
G= σ
L
ΔR = R o αΔθ
Voltage
(Ohm’s Law)
V = IR
P=
E
t
P = VI
2
P=I R
2
P=
Useful Constant Values:
*1 Ke = 8.988 x 109 Nm2C-2
*2 qelectron = 1.602 x 10-19 C
E = energy in Joules (J)
V = voltage in Volts (V)
R = resistance in Ohms (Ω)
ρ = resistivity in Ohm-meters (Ωm)
Change in Resistance
(due to change in
temperature)
Power
t = time in seconds (s)
V
R
G = conductance in Siemens (S)
σ = conductivity in Siemens per meter
(S/m)
A = cross section area of conductor in
meters squared (m2)
L = conductor length in meters (m)
P = power in Watts (W)
α = temperature coefficient of
resistance (K-1)
θ = temperature in degrees Kelvin (K)
Resistor Colour Coding
1 2 3
COLOUR
Black
Brown
Red
Orange
Yellow
Green
Blue
Violet
Grey
White
Gold
Silver
None
4
Example:
Blue, Yellow, Orange, Red
6, 4, 103, 2%
64,000Ω = 64kΩ ± 2%
BAND 1
(digit 1)
BAND 2
(digit 2)
BAND 3
(multiplier)
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
100
101
102
103
104
105
106
107
108
109
10-1
10-2
BAND 4
(tolerance)
1%
2%
5%
10%
20%
Resistors in Series and Parallel
Resistors in Series:
Subject
Equation
Variables and Units
Total
Resistance
R T = R1 + R 2 + R 3
R = resistance in Ohms
(Ω)
V = voltage in Volts (V)
Supply
Voltage
Vs = V1 + V2 + V3
Supply
Current
Is = I1 = I2 = I3
Total
Resistance
1
1
1
1
=
+
+
R T R1 R 2 R 3
Supply
Voltage
Vs = V1 = V2 = V3
Supply
Current
Is = I1 + I2 + I3
Resistors in Parallel:
I = Current in Amps (A)
Thevenin’s and Norton’s Theorems
Thevenin Equivalent Circuit:
Norton Equivalent Circuit: