Transcript
BASIC ELECTRICAL ENGINEERING FORMULAS
BASIC ELECTRICAL CIRCUIT FORMULAS
IMPEDANCE VOLT-AMP EQUATIONS
CIRCUIT
ELEMENT
absolute
value
complex
form
instantaneous
values
RMS values for
sinusoidal signals
ENERGY
(dissipated on R
or stored in L, C)
RESISTANCE R R v=iR Vrms=IrmsR E=Irms
2
R×t
INDUCTANCE 2πfL jωL v=L×di/dt Vrms=Irms×2πfL E=Li
2
/2
CAPACITANCE 1/(2πfC) 1/jωC i=C×dv/dt Vrms=Irms/(2πfC) E=Cv
2
/2
Notes:
R- electrical resistance in ohms, L- inductance in henrys, C- capacitance in farads, f - frequency
in hertz, t- time in seconds, π≈3.14159;
ω=2πf - angular frequency;
j - imaginary unit ( j
2
=-1 )
BASIC ELECTRICAL THEOREMS AND CIRCUIT ANALYSIS LAWS
LAW DEFINITION RELATIONSHIP
Ohm's Law modified
for AC circuits with
sinusoidal signals
Ù=Z×Ì, where Ù and Ì - voltage and
current phasors, Z - complex
impedance
(for resistive circuits: u=R×i )
Lorentz force law,
Faraday's law and Drude
model
Kirchhoff's Current
Law (KCL)
The sum of electric currents which
flow into any junction in an electric
circuit is equal to the sum of currents
which flow out
Conservation of electric
charge
Kirchhoff's Voltage
Law (KVL)
The sum of the electrical voltages
around a closed circuit must be zero
Conservation of energy
EQUATIONS FOR SERIES AND PARALLEL CONNECTIONS
CIRCUIT
ELEMENT
SERIES
CONNECTION
PARALLEL
CONNECTION
RESISTANCE
Rseries=
R1+R2+...
Rparallel=
1/
(1/R1+1/R2+...)
INDUCTANCE
Lseries=
L1+L2+...
Lparallel=
1/(1/L1+1/L2+...)
CAPACITANCE
Cseries=
1/
(1/C1+1/C2+...)
Cparallel=
C1+C2+...
RLC IMPEDANCE FORMULAS
CIRCUIT CONNECTION COMPLEX FORM ABSOLUTE VALUE
Series
Z=R+jωL+1/jωC
Parallel
Z=
1/(1/R+1/jωL+jωC)
MAGNETIC FIELD UNITS AND EQUATIONS
QUANTITY
SYM-
BOL
SI UNIT SI EQUATION
CGS
UNIT
CGS
EQUATION
CONVER-
SION
FACTOR
Magnetic
induction
B tesla (T) B=µ
o
(H+M)
Gauss
(G)
B = H+4πM
1 T =
10
4
G
Magnetic
field strength
H
ampere/
meter
(A/m)
H = NI/lc
( lc - magnetic
path, m)
Oersted
(Oe)
H = 0.4πNI/lc
(lc - magnetic
path, cm)
1 A/m =
4 π×10
-3
Oe
Magnetic flux Φ
weber
(Wb)
Φ = BAc
(Ac - area,
m
2
)
Maxwell
(M)
Φ = BAc
(Ac - area, cm
2
)
1 Wb =
10
8
M
Magnetization M
ampere/
meter
(A/m)
M=m/V
(m- total
magnetic
moment,
V- volume,
m
3
)
emu/cm
3
M=m/V
(m- total
magnetic
moment,
V- volume,
cm
3
)
1 A/m =
10
-3
emu / cm
3
Magnetic
permeability
of vacuum
µ
o
newton/
ampere
2
µ
o
= 4π×10
-7
1 - 4π×10
-7
Inductance L henry
L=µ
o
µN
2
Ac/lc
(N- turns,
Ac- area, m
2
,
lc - magnetic
path, m)
henry
L=
=0.4πµN
2
Ac/lc×
×10
-8
(N- turns,
Ac-area, cm
2
,
lc - magnetic
path, cm)
1
Emf (voltage) V volt
V= -NdΦ/dt
(N- turns)
volt
V= -10
-8
×
×N×dΦ/dt
(N- turns)
1
MAXWELL'S EQUATIONS IN FREE SPACE (IN SI UNITS)
LAW DIFFERENTIAL FORM INTEGRAL FORM
Gauss' law for
electricity
Gauss' law for
magnetism
Faraday's law
of induction
Ampere's law
NOTES: E - electric field, ρ - charge density, ε
0
≈ 8.85×10
-12
- electric permittivity of free space, π ≈ 3.14159,
k - Boltzmann's constant, q - charge, B - magnetic induction, Φ - magnetic flux, J - current density, i - electric
current,
c ≈ 299 792 458 m/s - the speed of light, µ
0
= 4π×10
-7
- magnetic permeability of free space, ▼ - del operator (if
V is a vector function, then ▼
.
V - divergence of V, ▼×V - the curl of V).
© 2009 Lazar Rozenblat
SMPS Power Supply Guide http://www.smps.us/ - tutorials, electronics reference,
formulas, schematics.
