Capacitors and Inductors

What you’ll learn: impedance, phasors, energy in reactive components, and practical non-ideal behaviour.

Prerequisites

• Basic circuit analysis and comfort with resistor networks
• Familiarity with frequency-domain concepts (see Filters chapter)

Learning objectives

• Calculate impedance of capacitors and inductors in the frequency domain
• Use phasor notation to solve simple AC circuits
• Build and measure LC resonance and observe non-ideal effects

Parts list

• Variety of capacitors (electrolytic and film)
• Small inductors (a few µH to mH)
• Resistors for test circuits
• Multimeter and optional LCR meter

Hands-On Mini Task: build an LC resonant circuit and observe resonance with a function generator or scope.

Diagram:

Step-by-step

1. Assemble a series or parallel LC circuit with known L and C values.
2. Drive the circuit with a swept sine source and monitor amplitude across the relevant component.
3. Identify the resonant frequency f0 = 1 / (2π√(LC)).
4. Observe bandwidth and note effects of component losses (Q factor).

Worked example

For L = 10 mH and C = 10 nF:

f0 = 1 / (2π√(LC)) = 1 / (2π × √(10e-3 × 10e-9)) ≈ 15.9 kHz.

Expected result

• A peak in amplitude at f0 for series resonance (or a dip for parallel depending on measurement point).
• Resonant sharpness depends on Q; real inductors and capacitors will broaden and shift the peak.

Navigation

• Previous: Filters and Frequency Response
• Next: Transient Analysis