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Electrical Theory

Electrical Theory. Quantity Symbol Unit Equation Charge Q coulomb Q = I Idt Current I ampere I = dQ/dt Voltage V volt V = dW/dQ Energy W joule W = I Vdt = I Pdt Power P watt P =dW/dt = IV Resistor R ohm V = IR Inductor L henry V = L dI/dt

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Electrical Theory

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  1. Electrical Theory QuantitySymbolUnitEquation 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 • Ohm’s Law • I =V/R (DC) I = V/Z (AC) • Kirchoff’s Law • Sum of Loop Voltages = 0 • Sum of Node Currents = 0 • Joule’s 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

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