Essential Reference

Circuit Logic Study Guide

Mastering the fundamentals of DC circuit analysis

Physics

Goal of Circuit Analysis

To determine the current (I) through and potential difference (V) across every component in a network using fundamental physical laws.

01

Ohm's Law

Describes the direct relationship between voltage and current for a linear resistor.

\[ V = I \cdot R \]

V = Volts (V) I = Amperes (A) R = Ohms (Ω)

Direct Relationship

\( I \propto V \) (at constant R)

Inverse Relationship

\( I \propto 1/R \) (at constant V)

V

I | R

Magic Triangle

02

Series & Parallel Architectures

Series: Single Path

Current (I) Same Everywhere

\[ I_{total} = I_1 = I_2 \]

Voltage (V) Divides/Adds

\[ V_{total} = V_1 + V_2 \]

Resistance (R) Summation

\[ R_{eq} = R_1 + R_2 \]

Ohm's Rule: Total voltage equals total current times equivalent resistance: \( V_{tot} = I \times R_{eq} \).

Parallel: Multi-Branch

Voltage (V) Same in Branches

\[ V_{total} = V_1 = V_2 \]

Current (I) Divides/Adds

\[ I_{total} = I_1 + I_2 \]

Resistance (R) Inverse Sum

\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} \]

Ohm's Rule: Each branch current is branch voltage divided by branch resistance: \( I_n = V_{tot} / R_n \).

03

Kirchhoff's Junction Rule

Conservation of Charge

At any node, the sum of entering currents equals the sum of leaving currents.

\[ \sum I_{in} = \sum I_{out} \]

IN OUT OUT

04

Kirchhoff's Loop Rule

Conservation of Energy

The energy supplied by sources must be completely used by resistors in a closed loop.

\[ \sum V_{loop} = 0 \text{ (or } V_{sources} = V_{drops}) \]

Rule 1: Loop Path

Pick any loop and a clockwise or counter-clockwise direction.

Rule 2: Polarity

Batteries (-) to (+) are GAINS. Traveling WITH current through R is a DROP.

Rule 3: Algebra

Sum all potential differences and set the result to zero.

05

Principle of Superposition

Essential for circuits with multiple active sources.

To Disable Voltage:

Short Circuit (0V)

Replace with a wire segment.

To Disable Current:

Open Circuit (0A)

Remove the branch entirely.

06

Electric Potential

Potential (V)

Energy per unit charge at a point.

\[ V = W / q \]

Potential Difference (\(\Delta V\))

Work done moving charge between points. Measured in Volts.

The Waterfall Analogy

Height = Electric Potential (V)
Water Flow = Current (A)
Rocks/Narrow Pipes = Resistance (Ω)

Circuit Logic Study Guide Rev 2

Circuit Logic Study Guide Rev 2

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