NapkinCalc

Electricity 2 — AC Circuits

Series RLC — impedance

continues from lesson 2 — values defined earlier in the course stay live here

the series RLC circuit analyzed below
the series RLC circuit analyzed below

ELI5: put R, L, and C in series and the two reactances fight — X_L pushes the voltage one way in time, X_C the other. What the source actually feels is the impedance, combining the resistance and the net reactance at right angles (Pythagoras again).

R1:=100ohmR_{1} := 100 ohm = 100 ohm
Zt=R12+(XL−XC)2Z_{t} = \sqrt{R_{1}^{2} + \left(X_{L} - X_{C}\right)^{2}} = 151.48 ohm total impedance
I1=VrmsZtI_{1} = \frac{V_{rms}}{Z_{t}} = 0.79356 A current the source must supply
ϕz=atan(XL−XCR1)\phi_{z} = \mathrm{atan}\left(\frac{X_{L} - X_{C}}{R_{1}}\right) = −0.8498-0.8498 phase angle — negative means the capacitor is winning