Circuits consist of discrete elements—resistors (R), capacitors (C), inductors (L), and sources—connected by ideal wires. Each element relates voltage to current in a specific way; understanding these relationships is essential for analyzing any circuit. An ideal circuit element is a two-terminal device whose behavior is completely characterized by its voltage–current relationship.
Start by observing real components and their datasheet specifications, then learn the ideal approximations. Practice drawing circuit symbols and labeling terminals with polarities and voltage/current directions.
Every circuit is built from a small set of ideal circuit elements — simplified mathematical models that capture the essential behavior of physical components. The key word is ideal: we ignore the imperfections of real parts to build a tractable theory. Once you understand ideal elements, you can reason about real circuits by treating parasitic effects as small corrections or additional elements added to the model.
A resistor is the simplest element: it relates voltage and current instantaneously through Ohm's law, V = IR. If you double the voltage across a resistor, the current doubles. Resistors dissipate energy as heat — they are the "lossy" elements. A voltage source maintains a fixed voltage across its terminals regardless of the current flowing through it; a current source maintains a fixed current regardless of the voltage. These are idealizations — real batteries have internal resistance, and real current sources have limits — but the ideal models are correct enough for most circuit analysis.
Capacitors and inductors are the energy-storing elements, and their behavior is fundamentally different from resistors: they relate voltage to current through derivatives rather than proportionality. A capacitor stores energy in an electric field between its plates, and its current depends on how quickly the voltage is changing: i = C(dv/dt). An inductor stores energy in a magnetic field around its coil, and its voltage depends on how quickly the current is changing: v = L(di/dt). Because they respond to *rates of change*, both elements care about *time* in a way resistors do not — this is what makes circuits with capacitors and inductors interesting and complex.
The concept of duality unifies capacitors and inductors mathematically: every statement about one has a mirror image in the other, with voltage and current swapped and C replaced by L. A capacitor blocks DC and passes AC; an inductor passes DC and blocks AC. A capacitor resists voltage changes; an inductor resists current changes. Learning these four element types — resistor, source, capacitor, inductor — and their defining voltage-current relationships is the foundation for every circuit analysis technique you will learn, from Kirchhoff's laws to frequency-domain methods.
This is a foundational topic with no prerequisites.
No prerequisites — this is a starting point.