Electrical Circuits on the FE Exam
Electrical circuit analysis appears on the FE Electrical exam as the highest-weighted single topic (9-14%) and also appears on the FE Other Disciplines and FE Mechanical exams as part of their engineering sciences sections. Whether you are an electrical engineering graduate or a mechanical engineer reviewing fundamentals, understanding circuit analysis is important for your FE exam score.
DC Circuit Fundamentals
Ohm's Law and Power
Ohm's Law states that voltage equals current times resistance (V = IR). Power can be expressed as voltage times current (P = VI), current squared times resistance (P = I squared times R), or voltage squared divided by resistance (P = V squared divided by R). These fundamental relationships form the basis for all circuit analysis.
Kirchhoff's Laws
Kirchhoff's Current Law (KCL) states that the sum of currents entering a node equals the sum of currents leaving that node. Kirchhoff's Voltage Law (KVL) states that the sum of voltage drops around any closed loop equals zero. These two laws, combined with Ohm's Law, allow you to solve any circuit.
Series and Parallel Circuits
Resistors in series add directly: total resistance equals the sum of individual resistances. Resistors in parallel combine using the reciprocal formula: the reciprocal of the total resistance equals the sum of the reciprocals of individual resistances. For two resistors in parallel, the equivalent resistance equals the product divided by the sum.
Network Theorems
Thevenin's Theorem
Any linear circuit can be replaced by an equivalent circuit consisting of a voltage source (Thevenin voltage) in series with a resistance (Thevenin resistance). Find the Thevenin voltage by calculating the open-circuit voltage at the terminals of interest. Find the Thevenin resistance by deactivating all independent sources and calculating the resistance seen from the terminals.
Norton's Theorem
Norton's theorem is the dual of Thevenin's theorem, replacing the circuit with a current source (Norton current) in parallel with a resistance (Norton resistance, equal to Thevenin resistance). The Norton current equals the short-circuit current at the terminals.
Superposition
In a linear circuit with multiple independent sources, the response (voltage or current) at any point equals the sum of the responses due to each source acting alone. When considering one source, replace other voltage sources with short circuits and other current sources with open circuits.
AC Circuit Analysis
AC circuits use sinusoidal voltages and currents described by amplitude, frequency, and phase angle. The key to AC analysis is using phasors and impedance to convert differential equations into algebraic equations.
Impedance
Impedance is the AC equivalent of resistance, expressed as a complex number. Resistor impedance is simply R (purely real). Inductor impedance is j times omega times L (purely imaginary, positive). Capacitor impedance is 1 divided by (j times omega times C), which equals negative j divided by (omega times C) (purely imaginary, negative). Omega is the angular frequency (2 times pi times frequency).
Phasor Analysis
Convert sinusoidal voltages and currents to phasor form (magnitude and angle). Apply KVL, KCL, and Ohm's Law using phasors and impedances exactly as you would for DC circuits. Then convert the phasor result back to the time-domain sinusoidal form.
AC Power
AC power analysis involves several power quantities:
- Real (Active) Power (P): Measured in watts, represents actual power consumed
- Reactive Power (Q): Measured in VARs, represents power stored and returned by inductors and capacitors
- Apparent Power (S): Measured in VA, equals the product of RMS voltage and RMS current
- Power Factor: The ratio of real power to apparent power, equals the cosine of the angle between voltage and current
The power triangle relates these quantities: apparent power is the hypotenuse, real power is the adjacent side, and reactive power is the opposite side. Power factor correction (adding capacitors to improve a lagging power factor) is a common practical application tested on the exam.
Transient Analysis
First-order RC and RL circuits produce exponential responses when switched. The time constant is RC for RC circuits and L/R for RL circuits. The general form of the response is the final value plus the difference between initial and final values times e to the negative t divided by the time constant.
Know how to find initial conditions (capacitor voltage cannot change instantaneously, inductor current cannot change instantaneously), final conditions (steady state after a long time), and the time constant for each circuit.