# alternating current

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1. Alternating Current NEOCLASSICAL 2. Alternating Current Waveforms NEOCLASSICAL 3. RMS Value RMS Root Mean square First square Then Take Mean Then Take Square root Mean of sin =0 Mean of sin2 = ( because sin2 = -cos 2x/2 , and average of cos2x= 0 , only Mean of Constant , K = K NEOCLASSICAL 4. For Sinusoidal waves only Vrms = 2 Vaverage = 0 Average of sinusoid is Zero NEOCLASSICAL 5. Root Mean Square of Sinusoid V= Vpeak cos ( w t + ) First step : Square V 2 peak cos 2( w t + ) Second step : Mean : V 2 peak / 2 Third step : Root = 2 NEOCLASSICAL 6. V = 3 + 4 cos (wt + 4) Vaverage = Average (3) + Average (4 cos (wt + 4)) = 3 + 0 = 3 V rms 1 . Square = 9 + 16 cos 2(wt + 4 ) + 24 cos (wt + 4) 2 . Mean = Mean(9) + Mean(16 cos 2(wt + 4 ) ) +Mean(24 cos (wt + 4) = 9 + (16/2) + 0 = 17 3 Root : 17 NEOCLASSICAL 7. Resistor V= Vpeak cos (t +) I = cos (t +) V I Current and Voltage are in phase for resistor NEOCLASSICAL 8. Inductor V= Vpeak cos (t +) Reactance of Inductor = XL=L I = cos (t +- 2 ) Current lags voltage by /2 V I NEOCLASSICAL 9. Voltage across inductor of 1 Henry = 200 cos (100t +), Find current w = 200 L = 1 Reactance = 200 Current peak = Vpeak / Reactance = 200/200 =1 Now current will be /2 behind voltage So , I =1 cos (100t + /2), If current is given Vpeak = Ipeak X Reactance = 1 X 200 =200 Current is /2 behind voltage voltage is /2 ahead V = 200 cos (100t + /2+ /2)= 200 cos (100t + ) NEOCLASSICAL 10. Capacitor V= Vpeak cos (t +) Reactance of Capacitor= Xc= I = (C)Vpeak cos (t ++ 2 ) Current leads voltage by /2 V I NEOCLASSICAL 11. GENERAL RLC CIRCUIT Input : V= Vpeak cos (t +) Current will have same form Except amplitude and phase I = Ipeak cos (t + + extra) This current will pass through all three as they are in series NEOCLASSICAL 12. Magnitude Phase, extra extra will be negative if XL > X c NEOCLASSICAL 13. I peak = extra = I = Ipeak cos (t + + extra) If Current is given Vpeak= Ipeak X Z Find extra and subtract NEOCLASSICAL 14. Power in RLC Power = () ( ) 2 cos(extra ) = V rms Irms cos(extra ) Power is lost only through Resistor NEOCLASSICAL 15. Resonance At resonance Amplitude is Max Z is minimum Frequency = / 2 NEOCLASSICAL 16. Quality Factor Greater the Q , sharper is the Resonance (i) is sharper NEOCLASSICAL