EC-1.3 Sinusoidal Steady State
You can analyse a circuit driven by a sinusoid using phasors and impedance, compute real and reactive power correctly, and find the resonant frequency and sharpness of a tuned circuit.
Under a steady sinusoid every voltage and current is a sinusoid of the same frequency, so only amplitude and phase are unknown. Representing those two numbers as one complex number turns differential equations into algebra, and every method from the earlier topics carries over unchanged with resistance replaced by impedance. The part that catches people is power: three different quantities are all called power here, and the one the meter charges you for is not the one the algebra hands you first.
Work through these
Phasors: amplitude and phase as one complex number, and why differentiation becomes multiplication
Writing a sinusoid as a complex amplitude turns the derivative into multiplication by the frequency variable, which is what removes the calculus. The physical signal is recovered by taking the real part at the end and never before.
NPTEL: Circuit Theory · CourseImpedance and admittance, and reusing node and mesh analysis unchanged
The inductor and the capacitor become impedances that depend on frequency, and every method from the resistive topics works exactly as before. Nothing new is learned here except that the numbers are complex.
Real, reactive and apparent power, and the power factor between them
Real power does work, reactive power sloshes back and forth without doing any, and apparent power is the product of the measured magnitudes. The angle between voltage and current decides the split, and it is what a power-factor correction capacitor changes.
MIT OpenCourseWare 6.002: Circuits and Electronics · CourseMaximum power transfer with complex impedances, and what conjugate matching means
The load that draws the most power is the complex conjugate of the source impedance, so its reactance cancels rather than matches. This is the rule every radio-frequency matching network exists to satisfy.
Series and parallel resonance: the frequency where the reactances cancel
At resonance the inductive and capacitive reactances cancel and the circuit looks purely resistive, which is a minimum impedance in series and a maximum in parallel. Knowing which is which decides whether the circuit passes or rejects that frequency.
NPTEL: Circuit Theory · CourseQuality factor and bandwidth, and the trade between them
A sharper resonance stores more energy per cycle relative to what it loses, and its passband is correspondingly narrower. Selectivity and bandwidth are the same number seen from two sides, which is why you cannot have both.
Sign in to keep your progress.
Free resources
We haven't checked most of these for screen reader use yet.
Links last checked 3 Sept 2026.
Stuck here?
Ask a mentor. A real person answers, and they can see exactly which topic you're on. Usually within a couple of working days.
Checking your session…
Topics shown in module order.