Circuit Theory and Components
Passive networks
Resistors combine simply: series R = R1 + R2 + …, parallel 1/R = 1/R1 + 1/R2 + …, and two in parallel give the product over the sum. Parallel combinations are always smaller than the smallest branch. Voltage dividers set bias and signal levels; a loaded divider must include the load in the calculation. Capacitors combine in the opposite way to resistors, and their reactance Xc = 1/(2πfC) falls as frequency rises. Inductive reactance Xl = 2πfL rises with frequency. Impedance combines resistance and reactance as a vector, Z = √(R² + X²).
Resonance and active devices
Series resonance occurs when Xl = Xc, at f = 1/(2π√(LC)); at resonance impedance is minimum in a series circuit or maximum in a parallel circuit, and circulating currents can be large. Transformers change voltage by the turns ratio and impedance by the square of that ratio. Diodes conduct one way, with a forward drop of about 0.6–0.7 V for silicon; transistors amplify or switch; filters use RC, LC or crystal elements to shape response.
Traps and rule of thumb
Examiners like resonance formula rearrangement, the square-law transformer trap, and questions that assume ideal components. Real capacitors have ESR and inductance; real inductors have winding resistance and self-capacitance. Remember that a capacitor blocks DC and passes AC, while an inductor passes DC and blocks AC.
Worked example: two 100 Ω resistors in parallel give 50 Ω. A 10 µH inductor with a 100 pF capacitor resonates at f = 1/(2π√(10⁻⁵ × 10⁻¹⁰)) ≈ 5.03 MHz.