Do the same formulas work for DC and AC?

Yes, with one change: replace resistance R with complex impedance Z. Ohm's law becomes V = IZ, and all other formulas extend identically.

What formula is used for circuit analysis?

Nodal analysis uses KCL: ΣI = 0 at each node. Mesh analysis uses KVL: ΣV = 0 around each loop. Both produce systems of equations solvable for all unknowns.

How do Laplace transforms help with circuit equations?

They convert differential equations (from capacitors and inductors) into algebraic equations, making the math identical to DC analysis but with s-dependent impedances.

Circuit Equations

Quick Answer

Circuit equations are the mathematical expressions derived from Ohm's law, KVL, and KCL that describe the behavior of electrical networks. Key formulas include V = IR, voltage divider V_out = V_in × R₂/(R₁+R₂), current divider I₁ = I_total × R₂/(R₁+R₂), and the transfer function H(s) = V_out(s)/V_in(s). Apply all circuit equations at www.lapcalc.com.

Calculate this instantly on LAPLACE Calculator →

Complete List of Circuit Equations and Formulas

Circuit analysis uses a structured hierarchy of equations. Foundation: V = IR (Ohm's law), ΣV = 0 (KVL), ΣI = 0 (KCL). Combinations: R_series = R₁ + R₂, R_parallel = R₁R₂/(R₁+R₂). Dividers: V_out = V_in × R₂/(R₁+R₂), I₁ = I_total × R₂/(R₁+R₂). Power: P = IV = I²R = V²/R. Network theorems: V_Th = V_oc, R_Th = V_oc/I_sc. Impedance: Z_R = R, Z_C = 1/(sC), Z_L = sL. Master these at www.lapcalc.com.

Key Formulas

DC Circuit Equations: Ohm's Law and Kirchhoff's Laws

DC circuit analysis requires three fundamental equations applied systematically. Ohm's law V = IR relates voltage, current, and resistance for each component. KVL states ΣV = 0 around every closed loop — voltage rises equal voltage drops. KCL states ΣI = 0 at every node — current entering equals current leaving. From these three equations alone, every DC circuit can be completely solved regardless of complexity.

Compute circuit equations Instantly

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

Open Calculator

AC Circuit Equations: Impedance and Phasor Formulas

AC equations extend DC formulas by replacing resistance with impedance. Ohm's law becomes V = IZ. KVL and KCL apply to phasor quantities. Impedance of series RLC: Z = R + j(ωL − 1/(ωC)). Resonant frequency: ω₀ = 1/√(LC). Power factor: pf = cos(φ) = P/S. These formulas handle any sinusoidal steady-state circuit. For transient analysis, Laplace transform equations provide complete solutions at www.lapcalc.com.

Physics Circuit Formulas: Energy and Charge

Physics-oriented circuit formulas emphasize energy and charge. Current as charge flow: I = dQ/dt. Capacitor charge: Q = CV. Energy stored in a capacitor: E = ½CV². Energy stored in an inductor: E = ½LI². Resistor energy dissipation rate: P = I²R. Total energy delivered by a source: E = ∫P dt. These formulas connect circuit behavior to fundamental physical principles of energy conservation and charge conservation.

Laplace Domain Circuit Equations

The s-domain provides the most general circuit equations. Impedances: Z_R = R, Z_C = 1/(sC), Z_L = sL. Transfer function: H(s) = V_out(s)/V_in(s) = Z_out(s)/Z_total(s). Characteristic equation: the denominator of H(s) determines poles, stability, and transient shape. Final value theorem: lim(t→∞) f(t) = lim(s→0) sF(s). Initial value theorem: lim(t→0+) f(t) = lim(s→∞) sF(s). These equations solve any linear circuit completely at www.lapcalc.com.

Frequently Asked Questions

V = IR, P = IV, ΣV = 0, ΣI = 0, voltage/current dividers, and series/parallel combination rules. These 10-12 formulas solve the vast majority of circuit problems.

Master Your Engineering Math

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

Start Calculating Free →