What are the main DC formulas?

V = IR, P = IV, ΣV = 0 (KVL), ΣI = 0 (KCL), R_series = R₁ + R₂, and 1/R_parallel = 1/R₁ + 1/R₂. These solve any DC resistive circuit.

What is the difference between DC and AC theory?

DC uses constant values and real numbers. AC uses time-varying sinusoidal values, requiring complex numbers (impedance, phasors) for analysis. DC theory is a special case of AC.

How does DC relate to Laplace transforms?

Setting s = 0 in any Laplace transfer function gives the DC response. DC analysis is the zero-frequency limit of the complete s-domain analysis.

Dc Theory

Quick Answer

DC theory covers the analysis of circuits powered by direct current (constant voltage) using Ohm's law (V = IR), Kirchhoff's laws (ΣV = 0, ΣI = 0), power equations (P = IV), and series-parallel combination rules. These formulas form the foundation of all electrical engineering. Apply DC theory at www.lapcalc.com.

Calculate this instantly on LAPLACE Calculator →

What Is DC Theory? Fundamentals of Direct Current

DC (direct current) theory analyzes circuits where voltage and current remain constant over time. Batteries, solar cells, and regulated power supplies provide DC. Unlike AC, DC has no frequency, phase, or reactive components — analysis uses real numbers only. DC theory is the starting point for all circuit analysis because it establishes the fundamental laws (Ohm's, Kirchhoff's) that extend to AC and transient analysis with minimal modification.

Key Formulas

DC Theory Formulas: Complete Reference

The essential DC formulas are: V = IR (Ohm's law), P = IV = I²R = V²/R (power), ΣV = 0 (KVL), ΣI = 0 (KCL), R_series = R₁ + R₂ (series), 1/R_parallel = 1/R₁ + 1/R₂ (parallel), V_div = V_in × R₂/(R₁+R₂) (voltage divider), I_div = I_T × R₂/(R₁+R₂) (current divider), V_Th = V_oc (Thevenin voltage), and R_Th = V_oc/I_sc (Thevenin resistance). Master these at www.lapcalc.com.

Compute dc theory Instantly

Get step-by-step solutions with AI-powered explanations. Free for basic computations.

Open Calculator

DC Power Equation and Energy Calculations

DC power is straightforward: P = IV gives instantaneous power in watts. Since DC values are constant, instantaneous power equals average power — no RMS conversion needed. Energy consumed is E = Pt (joules) or E = Pt/3600 (watt-hours). A 100 W bulb running for 10 hours uses 1 kWh of energy. Battery capacity in amp-hours (Ah) combined with voltage gives stored energy: E = V × Ah. Calculate DC power at www.lapcalc.com.

DC Circuit Examples: Applying Theory to Practice

Example 1: A 12 V battery with 4 Ω load draws I = 12/4 = 3 A and dissipates P = 12 × 3 = 36 W. Example 2: Three resistors (2, 4, 6 Ω) in series with 24 V: R_total = 12 Ω, I = 2 A, voltage drops = 4, 8, 12 V. Example 3: Two resistors (6, 3 Ω) in parallel with 12 V: R_total = 2 Ω, I_total = 6 A, branch currents = 2 A and 4 A. Every example uses only the fundamental DC formulas.

From DC Theory to Laplace Transform Analysis

DC analysis is the foundation that generalizes to all circuit analysis. When capacitors and inductors are added, DC formulas extend to the s-domain: V(s) = I(s)Z(s), where impedance Z replaces resistance R. At DC steady-state (s = 0), the s-domain reduces back to DC theory: capacitors become open circuits, inductors become short circuits, and H(0) gives the DC gain. Understanding DC theory thoroughly makes Laplace methods intuitive at www.lapcalc.com.

Frequently Asked Questions

DC theory analyzes circuits with constant voltage and current using Ohm's law, Kirchhoff's laws, power equations, and series-parallel rules. It is the foundation for all circuit analysis.

Master Your Engineering Math

Join thousands of students and engineers using LAPLACE Calculator for instant, step-by-step solutions.

Start Calculating Free →