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Electrical

Electrical Units

Ampere The constant current which when flowing through two parallel wires 1 m apart would produce in vacua a force of 2 x 10 -7 N/m A
Coulomb The quantity of if electricity when a current of 1 ampere flows for 1 second C
Volt The electromotive force or potential difference when a constant current of 1 ampere produces a heat in resistance at the rate of 1 newton-meter (joule)/second V
Ohm Is the electrical resistance of a conductor in which a constant curent of 1 ampere flow under a constant voltage of 1 volt ω
Henry The inductance in which 1 volt is produced by a currrent changing at the rate of 1 ampere/second H
Farad The Capacitance in which 1 couomb is stored for a potential difference of 1 volt F
Siemens The unit of electrical conductance S = A / V S
Joule The unit of energy work and quantity of heat. the work done when the point of application of a force of 1 newton is displaced through a distance of 1 metre in the direction of the force J
Watt The unit of power = t Joule/second W
Weber The unit of magnetic flux. The magnetic flux linking a circuit of one turn produces in it an electromotive force of 1 volt as it is reduced to zero at a uniform rate in 1 second Wb
Tesla The unit of magnetic flux density. The tesla is equal to 1 weber per square metre of circuit area T

Ohms law

E = Voltage (Volts)
I = Current (Amperes)
R = Resistance (Ohms)
W = Power (Watts)
E = I x R = Sqrt (W x R) = W / I
I = E / R = Sqrt( W / R) = W / E
R = E / I = W / I2 = E2 / W
W = E x I = E2 / R = I2 x R
 General Form of Ohms law
R = ρ . L / A
L = Length (metres),
A = Area (metre2,
ρ = resistivity (ω /metre)


Additive Resistances

Resistors in Series
R_total = R1 + R2 + R3...
Voltage across Resistors in Series
V_total = V_R1+V_R2+V_R3.. 		Resistors in Parallel
R_total = 1/ (1/R1 + 1/R2 +1/R3...)
The Voltage across Resistors in Parallel is the Same= V

Alternating Current Supplies

Alternating Voltage
e = e_max. sin ω. t = e_max .sin(f.t)
e_max = maximum voltage,
t = time (seconds),
ω = angular velocity rads/sec,
f = frequency (cycles /sec)

The Average value of a sinusoidal alternating quantity is calculated at 0.637x maximum value
The Root Mean Square(RMS) value of a sinusoidal alternating quantity is calculated at 0.707 x maximum value.
The form factor of a wave is the RMS value / Average Value = (for a sinusoidal wave) 1.1
The Peak (Crest) Factor is the Peak Value / RMS value = 1.414

Kirchoffs Laws

Kirchoffs First law.
The total current flowing towards a junction is equal to the total current flowing away from that junction.# i.e the algebraic sum of the currents flowing towards a junction is zero

Kirchoffs Second Law
In a closed circuit the algebraic sum of the products of the current and the resistance of each part of the circuit is equal to the resultant e.m.f in the circuit.

Capacitors

Q = V x C   therefore    I = C dV/dt
Q = Charge (coulomb)
V = Potential Difference (Volts)
C = Capacitance (Farad)
I = V / Xc
Xc = Capacitive Reactance (ω )
Xc = 1 / (2 p f C )
f = frequency (Herz)

Capacitors in Parallel
C_total. V = Q_total = Q1+Q2+Q3...
C_total. V = V.C1+V.C2+V.C3...
C_total = C1+C2+C3...
 Capacitors in Series
C_total = 1/ (1/C1+1/C2+1/C3...)

Inductances

V = L.dI/dt
L = Inductance (Henry)
 I = V/ XL
XL = Inductive Reactance (ω )
XL =2 p f L
f = frequency (Herz)

Additive Inductances

Inductances in Series
L_total = L1 + L2 + L3...
Inductances in Parallel
1 / L_total = 1 / L1 + 1 / L2 + 1 / L3 ...

Graphical Illustration of electrical Relationships

Useful relevant Links

  1. Alex's Resource Library... A site containing lots and lots of links to Electrical calculators, tutorials and information.
  2. L.M.Photonics Limited... Useful Power Calculations
  3. Mathconnet... Site includes various electrical Calculators
  4. Electricity In The woodshop ...An electrical Primer
  5. Electrical machines & Power Systems-by C. S. Indulkar ...Excel Solved Electrical Power Problems
  6. Metric Motors...Information / Dimensions of metric Motors
  7. Engineers Edge... -> Electrical Equations including 3 Phase power
  8. Monachos... -> A greek site with some useful electrical calculators
  9. Reliance... General Information on Range of Electric Motors AC/DC etc
  10. MotionNet... Wide range of supplier information and tutorials on drive systems

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Last Updated 07/06/2006