Electrical Theory

1
Electrical Theory

• Quantity Symbol Unit Equation
• Charge Q coulomb Q IIdt
• Current I ampere I dQ/dt
• Voltage V volt V dW/dQ
• Energy W joule W IVdt IPdt
• Power P watt P dW/dt IV
• Resistor R ohm V IR
• Inductor L henry V L dI/dt
• Capacitor C farad V 1/C IIdt

2
Electrical Theory

• Ohms Law
• I V/R (DC) I V/Z (AC)
• Kirchoff s Law
• Sum of Loop Voltages 0
• Sum of Node Currents 0
• Joules Law
• P IE I2R (I Squared R Loss)

3
Current Flow

• Electron Flow - From excess to deficient
• Conventional Current Flow
• Internal to Source (Battery)
• Negative to Positive
• External from Source (Battery)
• Positive to Negative
• Voltage Drop - Across a Resistor to -
• Negative Current - Assumed Direction Reversed

4
Equivalent Circuits

• Thevenin
• Two Terminal Resistor and Battery Circuit
• Series Voltage Source and Equivalent Resistor
• Voltage Source Open Circuit Voltage
• Equivalent Resistor V / Short Circuit Current
• Norton
• Two Terminal Resistor and Battery Circuit
• Parallel Voltage Source and Equivalent Resistor
• Current Source Short Circuit Current
• Equivalent Resistor V / Short Circuit Current

5
Series and Parallel Components

• Component Series Parallel
• R Req R1 R2 R3 1/Req 1/R1 1/R2 1/R3
• Z Zeq Z1 Z2 Z3 1/Req 1/Z1 1/Z2 1/Z3
• l Leq L1 L2 L3 1/Leq 1/L1 1/L2 1/L3
• C 1/Ceq 1/C1 1/C2 1/C3 Ceq C1 C3 C3

6
DC Circuit Components

• Component Impedance Current Power Energy
• R R I V/R None
• L Zero Infinite WL 1/2 LI2
• C Infinite Zero WC 1/2 CV2

7
AC Sinusoidal Analysis

• Resistor R I V/R P I2R V2/R
• Inductor jXL jwL I -jVL/wL QL I2XL
  VL2/XL
• Capacitor -jXC -j/wC I jVCwC QC I2XC
  VC2/XC
• Current I IR j IX
• Voltage V VR j VX
• Complex Power S VI (VR j VX)(IR
  - j IX)
• Complex Power S P j Q