AC, timing & reactive circuits
Waveforms, frequency, phase & RMS
Describe a changing signal without losing the big picture.
Period is the time for one cycle; frequency is cycles per second. Peak, peak-to-peak and RMS describe different aspects of amplitude. RMS tells you the equivalent heating effect in a resistor. A sine wave’s RMS is its peak divided by √2, but that shortcut does not apply to every shape or to a sine with DC offset. Phase compares timing within a cycle.
Impedance, phasors & resonance
Resistance is only one way a circuit opposes changing current.
Impedance combines resistance with reactance and includes phase. In sinusoidal steady state, an ideal inductor has ZL = jωL and a capacitor has ZC = 1/(jωC). The symbol j represents a 90° rotation in the complex plane. Inductor current lags its voltage; capacitor current leads. In a series RLC circuit, the two reactances cancel at resonance, leaving the resistance to limit current.
Time constants, charging & natural response
Understand why a circuit needs time to settle.
A capacitor stores energy in an electric field and an inductor in a magnetic field. Their state cannot change instantly without idealized infinite current or voltage. A first-order circuit approaches its final value exponentially. The time constant sets the pace, not a hard finishing time. RC circuits have τ = RC; a simple series RL circuit has τ = L/R.
Capacitors store energy, not just a voltage
Discover why doubling voltage matters more than doubling capacitance.
A capacitor stores energy in its electric field. Charge is Q = CV, but stored energy is E = ½CV². At constant capacitance, doubling voltage doubles charge and quadruples energy. At constant voltage, doubling capacitance doubles both. A disconnected capacitor may still hold charge; removing power does not prove that a circuit is discharged.