Basic Electrical Engineering
This area covers DC and AC circuit fundamentals and the laws that govern them — knowledge every discipline needs for instrumentation, motors, and power. The FE keeps it quantitative but tractable: Ohm's law, power, series–parallel reduction, Kirchhoff's laws, capacitors and inductors, and the essentials of AC and three-phase power.
Ohm's law and electrical power
Ohm's law relates voltage, current, and resistance: V = I·R. A 10 Ω resistor carrying 2 A drops V = 20 V. Power dissipated as heat has three equivalent forms: P = V·I = I²·R = V²/R. A 4 Ω resistor at 3 A dissipates I²·R = 9·4 = 36 W; a 6 Ω resistor across 12 V dissipates V²/R = 144/6 = 24 W. These relations size conductors and predict heating. Choosing the power form that uses the two quantities you already know avoids solving for a third variable unnecessarily.
Series and parallel resistances
In series, the same current flows through each element and resistances add: R_eq = R₁ + R₂ + R₃, so 2 + 3 + 5 = 10 Ω. In parallel, the same voltage appears across each branch and conductances add: 1/R_eq = Σ(1/Rᵢ), giving a result smaller than the smallest branch. Two 10 Ω resistors in parallel give 5 Ω; a 6 Ω and 3 Ω in parallel give (6·3)/(6+3) = 2 Ω. The product-over-sum shortcut works only for exactly two resistors. Recognizing which elements share current (series) versus voltage (parallel) is the crux.
Kirchhoff's laws and dividers
Kirchhoff's voltage law (KVL) states that the algebraic sum of voltages around any closed loop is zero (energy conservation); Kirchhoff's current law (KCL) states that current into a node equals current out of it (charge conservation). From KVL comes the voltage divider: across series resistors, each takes a share of the source proportional to its resistance — 12 V across 4 Ω and 8 Ω puts 4 V on the 4 Ω and 8 V on the 8 Ω. The current divider does the analogous thing for parallel branches. These are the workhorses for analyzing any resistive network.
Capacitors and inductors
A capacitor stores energy in an electric field, Q = C·V and E = ½·C·V²; capacitors combine oppositely to resistors — in parallel they add, in series 1/C_eq = Σ(1/Cᵢ). Two 4 µF capacitors in series give 2 µF. An inductor stores energy in a magnetic field, E = ½·L·I², and combines like resistors (series adds). Both are energy-storage (reactive) elements whose voltage–current relations involve rates of change, producing the transient RC and RL responses that settle over a time constant τ = R·C or L/R.
AC circuits and impedance
Alternating current varies sinusoidally; its effective (RMS) value is V_peak/√2 for a sine wave, the value that delivers the same average power as an equivalent DC source. Capacitors and inductors present frequency-dependent reactance (X_C = 1/(ωC), X_L = ωL), which combines with resistance into complex impedance Z = R + jX. Impedance shifts the phase between voltage and current; the power factor cos φ is the fraction of apparent power that becomes real power. Real power P = V·I·cos φ is what does useful work, while reactive power circulates without net energy transfer.
Three-phase power
Balanced three-phase systems deliver power more efficiently and smoothly than single-phase, which is why they run industrial motors and the grid. Sources and loads connect in either wye (Y) or delta (Δ). In a wye connection, line-to-line voltage is √3 times the line-to-neutral voltage (V_LL = √3·V_LN), while line and phase currents are equal; in delta the relationships swap. Total three-phase real power is P = √3·V_LL·I_L·cos φ. Keeping the √3 factor and the wye/delta distinctions straight is what these problems test.
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