https://engineers.academy/product/l3-nd-engineering-principles-exam-preparation/ Level 3 Engineering Principles - DC Circuits Info and Equations

1. LEVEL 3 ENGINEERING PRINCIPLES - DC CIRCUITS INFORMATION AND EQUATIONS
Voltage, Current, Power and Resistance
Subject Equation Variables and Units
Force between charged
particles (Coulombs Law) F =
keq1q2
r2
F = [attractive or repulsive] force in
Newtons (N)
*1
Ke = Coulomb’s constant (Nm2
C-2
)
*2
q = particle charge in Coulombs (C)
r = distance between particles (m)
I = Current in Amps (A)
Q = [total] charge in Coulombs (C)
t = time in seconds (s)
E = energy in Joules (J)
V = voltage in Volts (V)
R = resistance in Ohms (Ω)
ρ = resistivity in Ohm-meters (Ωm)
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)
Current I =
Q
t
Energy E = QV
Resistance R = ρ
L
A
Conductance G = σ
A
L
Change in Resistance
(due to change in
temperature)
ΔR = RoαΔθ
Voltage
(Ohm’s Law)
V = IR
Power
P = Et
P = VI
P = I2
R
P =
V2
R
Useful Constant Values:
*1 Ke = 8.988 x 109 Nm2C-2
*2 qelectron = 1.603 x 10-19 C

2. Resistor Colour Coding
Example:
Blue, Yellow, Orange, Red
6, 4, 103, 2%
64,000Ω = 64kΩ ± 2%
COLOUR
BAND 1
(digit 1)
BAND 2
(digit 2)
BAND 3
(multiplier)
BAND 4
(tolerance)
Black 0 0 100
Brown 1 1 101 1%
Red 2 2 102 2%
Orange 3 3 103
Yellow 4 4 104
Green 5 5 105
Blue 6 6 106
Violet 7 7 107
Grey 8 8 108
White 9 9 109
Gold 10-1 5%
Silver 10-2 10%
None 20%
1 2 3 4

3. Resistors in Series and Parallel
Subject Equation Variables and Units
Resistors in Series: Total
Resistance
RT = R1 + R2 + R3
R = resistance in Ohms
(Ω)
V = voltage in Volts (V)
I = Current in Amps (A)
Supply
Voltage
Vs = V1 + V2 + V3
Supply
Current
Is = I1 = I2 = I3
Resistors in Parallel:
Total
Resistance
1
RT
=
1
R1
+
1
R2
+
1
R3
Supply
Voltage
Vs = V1 = V2 = V3
Supply
Current
Is = I1 + I2 + I3

4. Capacitor Equations
Subject Equation Variables and Units
Electric Flux Density
(on Capacitor Plates) D =
Q
a
D = electric flux density in
Coulombs per square meter (C/m2)
Q = charge in Coulombs (C)
a = capacitor common plate area in
square meters (m2)
C = capacitance in Farads (F)
V = voltage in Volts (V)
d = distance between capacitor
plates in meters (m)
*ε0 = absolute permittivity
εr = relative permittivity
E = energy stored in Joules (J)
τ = time constant in seconds (s)
R = resistance in ohms (Ω)
Vc = voltage across capacitor
(during charging) in volts (v)
Vs = supply voltage in volts (v)
t = time under charge / discharge
in seconds (s)
Vd = voltage across capacitor
(during discharging) in volts (v)
Capacitance
C =
Q
V
C = (
a
d
) ε0εr
Energy Stored by a
Capacitor
E =
QV
2
E =
CV2
2
Capacitor Time Constant
(Charging and Discharging
through a Resistor)
τ = RC
Capacitor Charging
Voltage
Vc = Vs (1 − e
−t
τ )
Capacitor Discharging
Voltage Vd = Vse
−t
τ
Useful Constant Values:
*ε0 = 8.85 x 10-12

5. Capacitors in Series and Parallel
Subject Equation Variables and Units
Capacitors in Series: Total
Capacitance
1
CT
=
1
C1
+
1
C2
+
1
C3
C = capacitance in
Farads (F)
Q = charge in Coulombs
(C)
V = voltage in Volts (V)
Total
Charge
QT = Q1 = Q2 = Q3
Supply
Voltage
Vs = V1 + V2 + V3
Capacitors in Parallel:
Total
Capacitance
CT = C1 + C2 + C3
Total
Charge
QT = Q1 + Q2 + Q3
Supply
Voltage
Vs = V1 = V2 = V3