# Unit 01: Basic Electrical Math and Formulas

## Fractions

• 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

## 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, Series-Parallel, or Multi-wire branch
• Grounding wire is ╧
• Grounded wire is Neutral
• Ungrounded wire is Hot / Live
• ### Basic electrical circuit is:

• Power Source
• Conductor
• Protection Device
• Switch

• Voltage
• Current
• Resistance
• Power

### 3-wire, 1Ø Circuit_Determine Current in Neutral

• In = L1 – L2
• In = current neutral
• Current in Neutral = Difference between current flow of L1 and L2
• Balanced system in a 3-wire, 1Ø and all 3Ø circuits is when Neutral current equals zero.
• In = L1 – L2 = 0
• Hot wires all have equal current flowing

### 3 or 4-wire, 3Ø Circuit_Determine Current in Neutral

• In = √(L12 + L22 + L32) – [(L1 x L2) + (L2 x L3) + (L1 x L3)]

### Voltage Drop

 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 – Electro-Magnetic Field
• Capacitor – Electrical Field

#### AC values of wave forms/Sine waves

1. Instantaneous is any value in time measured on a sine wave.  Ranges from -peak to 0 to +peak
2. Peak is maximum value of a voltage or current sine wave
3. Effective Voltage / Effective Current is same amount of heat in resistors equivilent to VDC or DC current

#### RMS determines effective voltage or current value

1. Square instantaneous values
• Determine the Mean(average) of all instantaneous values
2. convert negatives values to positve
3. 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:

1. Plate Distance
• Capacitance is inversely proportional to the distance between capacitor plates
2. 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
3. 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 AC-current waveform transforms through a full-wave bridge rectifier into pulsating direct-current waveform whereby a capacitor smooths out the direct-current waveform resulting in near-steady direct-current
• Adding circuit capacitors
• counteracts high inductance
• increases power factor

### Capacitive Reactance (XC) (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
• XC = 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 electro-magnetic 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

### Counter-Electromotive 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 cross-sectional area
• CEMF is inversely proportional to core’s length

### Inductive Reactance

• Inductive Reactance is self-induced voltage (aka CEMF) acting to oppose the change in current flowing in conductors
• Measured in Ohms
• Expressed using XL
• XL = 2 * π * f * L
• XL
• 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 cross-sectional area = 4X resistance
• Inversely proportional to conductor cross-sectional area
• Larger diameter = lower resistance
• 2X diameter = 4X cross-sectional area = 1/4 resistance

### AC Circuit Conductor Resistance

• Current and voltage affected by:
1. resistance (same as DC Circuit Conductor Resistance)
2. Eddy Currents
3. 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 cross-sectional area
• CEMF is inversely proportional to core’s length

### 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
• Transformers, motors, generators, etc.
• #### Power Factor / True Power (W) / Apparent Power (VA)

1. Apparent Power (VA)
2. True Power (W)
3. 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