Electrical Fundamentals and DC Circuits

FE Exam Weight: Basic Electrical Engineering accounts for 6-9 questions (~7% of the exam). Focus on circuit analysis using Ohm's Law and Kirchhoff's laws.

Fundamental Quantities

Ohm's Law

$V = IR$

Power

$P = VI = I^2R = \frac{V^2}{R}$

Energy consumption: E = P × t

• 1 kWh = 1,000 W × 3,600 s = 3.6 × 10⁶ J

Kirchhoff's Laws

KCL (Current Law) — At any node:

$\sum I_{in} = \sum I_{out}$

The algebraic sum of currents at any junction is zero.

KVL (Voltage Law) — Around any closed loop:

$\sum V = 0$

The algebraic sum of voltages around any closed loop is zero.

Series and Parallel Circuits

Resistors in Series

$R_{total} = R_1 + R_2 + R_3 + \cdots$

• Same current flows through all resistors
• Voltage divides: V₁ = IR₁

Resistors in Parallel

$\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \cdots$

Two resistors in parallel: $R_{total} = \frac{R_1 R_2}{R_1 + R_2}$

• Same voltage across all resistors
• Current divides: I₁ = V/R₁

Voltage Divider

$V_x = V_{total} \cdot \frac{R_x}{R_{total}}$

Current Divider (two resistors in parallel)

$I_1 = I_{total} \cdot \frac{R_2}{R_1 + R_2}$

DC Circuit Analysis Methods

Node Voltage Method

1. Choose a reference node (ground)
2. Label voltages at all other nodes
3. Write KCL at each node (express currents using Ohm's law)
4. Solve the system of equations

Mesh Current Method

1. Assign a current loop to each mesh (independent loop)
2. Write KVL around each mesh
3. Solve the system of equations

Thevenin's Theorem

Any linear circuit can be replaced by a voltage source Vth in series with a resistance Rth:

• Vth = open-circuit voltage at the terminals
• Rth = resistance seen from the terminals with all sources deactivated (voltage sources shorted, current sources opened)

Norton's Theorem

Any linear circuit can be replaced by a current source IN in parallel with a resistance RN:

• IN = short-circuit current at the terminals
• RN = Rth (same Thevenin resistance)

Superposition

In a linear circuit with multiple sources, the contribution of each source can be found independently, then added. Deactivate all other sources while analyzing each one.