LEVEL 3 ENGINEERING PRINCIPLES - DC CIRCUITS INFORMATION AND EQUATIONS
Voltage, Current, Power and Resistance 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 = Et P = VI 2
P=I R V2 P= R
Useful Constant Values: *1 Ke = 8.988 x 109 Nm2C-2 *2 qelectron = 1.603 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)
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 (Ί) 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)
Capacitor Equations Subject Electric Flux Density (on Capacitor Plates)
Equation
D=
C=
Variables and Units
Q a
D = electric flux density in Coulombs per square meter (C/m2)
Q V
a = capacitor common plate area in square meters (m2)
Q = charge in Coulombs (C)
Capacitance
a C = ( ) ε0 εr d E= Energy Stored by a Capacitor
Capacitor Time Constant (Charging and Discharging through a Resistor) Capacitor Charging Voltage Capacitor Discharging Voltage
Useful Constant Values:
*ε0 = 8.85 x 10-12
QV 2
d = distance between capacitor plates in meters (m)
εr = relative permittivity E = energy stored in Joules (J) τ = time constant in seconds (s) R = resistance in ohms (Ω)
τ = RC
Vd =
V = voltage in Volts (V)
*ε0 = absolute permittivity
CV 2 E= 2
Vc = Vs (1 −
C = capacitance in Farads (F)
Vc = voltage across capacitor (during charging) in volts (v) −t eτ)
−t Vs e τ
Vs = supply voltage in volts (v) t = time under charge / discharge in seconds (s) Vd = voltage across capacitor (during discharging) in volts (v)
Capacitors in Series and Parallel
Capacitors in Series:
Subject
Equation
Variables and Units
Total Capacitance
1 1 1 1 = + + CT C1 C2 C3
C = capacitance in Farads (F)
Total Charge
Q T = Q1 = Q 2 = Q 3
Q = charge in Coulombs (C) V = voltage in Volts (V)
Supply Voltage
Vs = V1 + V2 + V3
Total Capacitance
CT = C1 + C2 + C3
Total Charge
Q T = Q1 + Q 2 + Q 3
Supply Voltage
Vs = V1 = V2 = V3
Capacitors in Parallel: