Unit 01: Basic Electrical Math and Formulas
Fractions
 Adding:
 Step 1: Denominators are the same
 Step 2: Add the numerators
 Step 3: Simplify
 (I.E. Want to add: 1/11 + 2/3? The LCM of 3 and 11 is 33 . Multiply the numerator and denominator of 1/11 by 3 , and multiply the numerator and denominator of 2/3 by 11)
 Convert to Decimal Number:
 Numerator / Denominator
Percentages
 Conversions
 to Whole/Decimal numbers
 Move decimal point two to left
 Multiplier
 Convert % to Whole number or decimal , then Multiply
 Increase or decrease:
 Convert % to Whole number or decimal , then add 1.0 to decimal, then multiply
 to Whole/Decimal numbers
Reciprocals
 Convert number to a fraction with 1/ as the numerator
 For percentages:
 Convert percentage to decimal
 Divide 1 by resultant decimal
Unit 02: Electrical Circuits
NEC Article
 Current flow is Series, Parallel, SeriesParallel, or Multiwire branch
 Grounding wire is ╧
 Grounded wire is Neutral
 Ungrounded wire is Hot / Live

Basic electrical circuit is:
 Power Source
 Conductor
 Load
 Protection Device
 Switch

Electrical circuit problemsolving is for:
 Voltage
 Current
 Resistance
 Power
3wire, 1Ø Circuit_Determine Current in Neutral
 I_{n} = L_{1} – L_{2}
 I_{n} = current neutral
 Current in Neutral = Difference between current flow of L_{1} and L_{2}
 Balanced system in a 3wire, 1Ø and all 3Ø circuits is when Neutral current equals zero.
 I_{n} = L_{1} – L_{2} = 0
 Hot wires all have equal current flowing
3 or 4wire, 3Ø Circuit_Determine Current in Neutral
 I_{n} = √(L_{1}^{2} + L_{2}^{2} + L_{3}^{2}) – [(L_{1} x L_{2}) + (L_{2} x L_{3}) + (L_{1} x L_{3})]
Voltage Drop
 Voltage drop across each resistor
 Voltage Drop is dependent on the magnitude of the current and conductor resistance
 https://www.mikeholt.com//technnicalvoltagedropcalculationspartone.php
Material Resistance  DC Voltage  AC Voltage 
Inductive Reactance  
Capacitive Reactance  
Unit 03: Alternating Current
NEC Article
Alternating Current (AC) is used to transmit electricity cheaply at high voltage and low current
 less voltage drop
 conductors and equipment can be smaller and cheaper
 Energy Storage means:
 Inductor – ElectroMagnetic Field
 Capacitor – Electrical Field
AC values of wave forms/Sine waves
 Instantaneous is any value in time measured on a sine wave. Ranges from peak to 0 to +peak
 Peak is maximum value of a voltage or current sine wave
 Effective Voltage / Effective Current is same amount of heat in resistors equivilent to VDC or DC current
RMS determines effective voltage or current value
 Square instantaneous values
 Determine the Mean(average) of all instantaneous values
 convert negatives values to positve
 Calculate square root value of the Mean
 reverses the numerical effect of squaring the values in step 1
Capacitance
 Capacitance is the property the stores & releases electrical energy using an electrical field.
 Capacitive Reactance is a
Capacitors
 Direct current can not flow through a capacitor
 Permits current to flow by the ability to store and discharge energy as alternating current flows in opposite directions
 Resists changes in current
 Introduces reactance to a circuit
 Shifts Sine wave to current leading voltage by 90
 Voltage lags current wave form by 90
A capacitor resists changes in voltage or changes in current
Capacitor capacitance factors:
 Plate Distance
 Capacitance is inversely proportional to the distance between capacitor plates
 Surface Area
 Capacitance is directly proportional to surface area
 Capacitors in Parallel increases the capacitance by the sum of the capacitors
 Capacitors in series increases the dielectric and decreases the capacitance
 Capacitance is directly proportional to surface area
 Dielectric Strength
 The maximum voltage that can be applied across the dielectric before it shorts out (fails)
Capacitor Uses:
 Momentary current flow to a capacitors prevents arcing across a switch during opening/closing
 Source ACcurrent waveform transforms through a fullwave bridge rectifier into pulsating directcurrent waveform whereby a capacitor smooths out the directcurrent waveform resulting in nearsteady directcurrent
 Adding circuit capacitors
 counteracts high inductance
 increases power factor
Capacitive Reactance (X_{C) }(Ω)
 Capacitive Reactance is the opposition to alternating current flow by capacitors , expressed in Ω using Xc
 Capacitive Reactance is when alternating current sine wave reached + peak & a capacitor fully charges to the same polarity. As the sine wave decreases heading to – peak, the capacitor discharges which has the effect of resisting changes in alternating current circuit voltage.
 Voltage Lags Current
 X_{C} = ^{1}/_{(2 * π * f * C)}
 Xc is Ω
 π is 3.14
 f = frequency / hertz
 C = capacitance / farads
Induction
 Inductance is an electrical circuit property which stores and releases electrical energy using an electromagnetic field
 Induced Current is the movement of electrons caused by an external magnetic field
 Induced Voltage is the associated potential of the movement of electrons caused by an external magnetic field
 Induction uses:
 Transformers
 Motors
 Generators
CounterElectromotive Force (CEMF)
 90° out of phase with circuit current
 180° out of phase with applied voltage
 CEMF either opposes or aids conductor current flow
 AC current increases CEMF opposing conductor current preventing current increases
 AC current decreases CEMF aiding conductor current preventing current decreases
 CEMF created within a winding is directly proportional to:
 current flow
 The winding
 Conductor length
 number of turns
 Frequency
 Increasing winding current
 increased alternating magnetic field
 CEMF
 Increasing the number of winding loops & the closer the winding loops are
 increases CEMF
 Increasing the frequency
 increase CEMF
 Soft, iron core within windings increases CEMF compared to air core
 CEMF is directly proportional to winding core crosssectional area
 CEMF is inversely proportional to core’s length
Inductive Reactance
 Inductive Reactance is selfinduced voltage (aka CEMF) acting to oppose the change in current flowing in conductors
 Measured in Ohms
 Expressed using X_{L}
 X_{L} = 2 * π * f * L
 X_{L}
 π is 3.14
 f = frequency / hertz
 L = Inductance / henrys
Efficiency
Energy efficiency is the ratio of its useful power output to its total power input
Total amount of power loss in watts
Expressed in percentage (%)
How much input energy is used for the intended purpose
Ratio of output true power to input true power
Output power never greater then input power; Output always less than input
Efficiency factor always 1 or less (100% or less)
P= I2R = Power/heat losses
DC Circuit Conductor Resistance
 Current and voltage affected only by resistance
 Directly proportional to conductor length
 If conductors length doubles, total resistance doubles
 Smaller diameter = higher resistance
 1/2 diameter = 1/4 crosssectional area = 4X resistance
 Inversely proportional to conductor crosssectional area
 Larger diameter = lower resistance
 2X diameter = 4X crosssectional area = 1/4 resistance
AC Circuit Conductor Resistance
 Current and voltage affected by:
 resistance (same as DC Circuit Conductor Resistance)
 Eddy Currents
 Skin Effect
 Eddy Currents
 small, independent currents resulting from the expanding and collapsing magnetic field
 Flows erratically
 Consumes power
 Increases opposition to current flow
 Greatest at conductors center
 Skin Effect
 Expanding and collapsing magnetic field induced voltage in conductors which repels flowing electrons towards the conductor surface
 Applied AC current flows towards conductor surface
 Increases opposition to current flow
 Stranded conductors reduce skin effect
 Conductor Windings
 CEMF created within a winding is directly proportional to:
 current flow
 The winding
 Conductor length
 number of turns
 Frequency
 Increasing winding current
 increased alternating magnetic field
 CEMF
 Increasing the number of winding loops & the closer the winding loops are
 increases CEMF
 Increasing the frequency
 increase CEMF
 Soft, iron core within windings increases CEMF compared to air core
 CEMF is directly proportional to winding core crosssectional area
 CEMF is inversely proportional to core’s length
 CEMF created within a winding is directly proportional to:
Power Factor
 Inductive Reactance
 Voltage leads current
 Capacitive Reactance
 Current leads voltage

Unity Power Factor
 ‘Perfect Power Factor’ of 1 (100%)
 Voltage and current are in phase
 both reach 0 and peak value at same time
 no leading or lagging
 PF = 1.00 = 100%
 Achieved with power supplied to a pure resistive load
 incandescent light bulb
 heating element
Apparent Power (VA)
 Power supplied to circuit by the source determined by measuring voltage and current in an inductive or capacitive circuit and then multiplying together
 Measured in kVA
 Apparent Power (VA) is greater then True Power (W)
 Use VA to size circuits and equipment
 Fewer loads can be supplied using VA than W
 Larger circuits, panels, and transformers may be required
 Inductive loads
 Transformers, motors, generators, etc.

Power Factor / True Power (W) / Apparent Power (VA)
 Apparent Power (VA)
 True Power (W)
 Power Factor (PF)
 Apparent Power (VA) = W / PF
 also VA = kW / PF
 also VA = E*I (Apparent Power = Volts * Amps)
 True Power (W) = VA * PF
 Power Factor (PF) = W / VA
 also PF = KW / kVA
True Power (W)
 Measured in KW
 Resistive loads
 incandescent light bulbs, heating elements, etc.