NapkinCalc

Electricity 2 — AC Circuits

Reactance — resistance that depends on frequency

continues from lesson 1 — values defined earlier in the course stay live here

ELI5: an inductor hates changing current — the faster the change, the harder it pushes back, so its reactance X_L = 2π·f·L rises with frequency. A capacitor is the mirror image: it blocks DC completely but waves fast signals through, so X_C = 1/(2π·f·C) falls with frequency.

fline:=60Hzf_{line} := 60 Hz = 60 Hz
L1:=50e−3HL_{1} := 50e-3 H = 0.05 H a 50 mH inductor
C1:=20e−6FC_{1} := 20e-6 F = 0.00002 F a 20 µF capacitor
XL=2⋅π⋅fline⋅L1X_{L} = 2 \cdot \pi \cdot f_{line} \cdot L_{1} = 18.85 ohm inductive reactance at 60 Hz
XC=12⋅π⋅fline⋅C1X_{C} = \frac{1}{2 \cdot \pi \cdot f_{line} \cdot C_{1}} = 132.63 ohm capacitive reactance at 60 Hz

Real-world hook: frequency-dependent reactance is how a crossover sends bass to the woofer and treble to the tweeter, and how a power supply filter blocks hum.

Try it yourself: the inductive reactance of a 0.1 H coil at 60 Hz? (X_L = 2π·f·L.)

XLyou:=2∗π∗60Hz∗0.1HXL_{you} := 2 * \pi * 60 Hz * 0.1 H = 37.699 ohm ✏️ Your turn: compute 2π · 60 Hz · 0.1 H. The result comes out in ohms.
✓ pass abs(XLyou−2∗π∗60Hz∗0.1H)<0.1ohmabs(XL_{you} - 2 * \pi * 60 Hz * 0.1 H) < 0.1 ohm green when your reactance is correct