resistorinductorcapacitor

Resistor, inductor, and capacitor are the three fundamental passive components used to control and shape electrical signals. A resistor (R) opposes current flow in proportion to the voltage across it, described by Ohm's law V = IR. Resistors dissipate electrical power as heat, with P = I^2R = V^2/R in ideal cases. In most circuits their resistance remains constant over a wide range of operating conditions, though real components exhibit parasitic effects.

An inductor stores energy in a magnetic field created by current through a coil. Its defining relation is V = L di/dt, where L is inductance. In alternating current (AC) analysis, an inductor presents impedance Z_L = jωL, increasing with frequency. The energy stored is W = (1/2)LI^2. Inductors resist rapid changes in current and are used in filtering, energy storage, and waveform shaping.

A capacitor stores energy in an electric field between two conductors separated by a dielectric. Its defining relation is i = C dv/dt, where C is capacitance. In AC circuits, a capacitor presents impedance Z_C = 1/(jωC), decreasing with frequency. The energy stored is W = (1/2)CV^2. Capacitors are used for coupling, decoupling, timing, and filtering, and as energy storage elements in power supplies.

Together, these components form a wide range of networks. In series or parallel configurations, they create filters (low-pass, high-pass, band-pass, notch), timing circuits, and resonant systems. Common time constants include τ = RC for RC circuits and τ = L/R for RL circuits, while LC circuits exhibit resonant frequency ω0 = 1/√(LC) (f0 = 1/(2π√(LC))).