Alternating Current

AC Voltage Applied to an Inductor, Capacitor


  •  AC voltage is applied across R – C series, then the impendence is given by \tt Z=\sqrt{\frac{1}{c^{2}\omega^{2}}+R^{2}}
  • AC voltage applied across R – C series, then the phase difference between emf and current is given by \tt \phi=tan^{-1}\left(\frac{1}{c\omega}/R\right)
  • AC voltage applied across L – C – R series, the instantaneous alternating current is given by i = io sin (wt ± φ)
  • AC voltage applied across L – C – R series, then the maximum current is \tt i_{0}=\frac{e_{0}}{z}
  • AC voltage applied across L – C – R series, then the impendence is given by \tt Z=\sqrt{\left(L\omega-\frac{1}{\omega c}\right)+R^{2}}
  • AC voltage applied across LCR series, then the phase difference between emf and current is given by \tt \phi=\tan^{-1}\frac{\left(L\omega-\frac{1}{\omega c}\right)}{R}
  • If \tt L\omega>\frac{1}{L\omega} ; φ is positive
    Voltage leads current by φ
    Circuit is predominantly Inductive
  • If \tt \frac{1}{\omega c} > {L\omega} ; φ is negative
    Current leads voltage by φ
    Circuit is predominantly capacitive
  • If \tt L\omega = \frac{1}{\omega c} ; φ is zero
    Voltage and current are in phase
    This condition is called RESONANCE
    At resonance \tt \omega_{0}=\frac{1}{\sqrt{LC}}
    \tt n_{0}=\frac{1}{2\pi\sqrt{LC}}
  • Resonant circuits are used in tuning mechanism of radio (or) TV and in musical instruments.
  • In R,C circuit, \tt V_{RC}=\sqrt{V_R^2+V_C^2} \because VC is \frac{\pi}{2} out of phases of VR.
  • In L,R circuit, \tt V_{LR}=\sqrt{V_L^2+V_R^2} \because VL is \frac{\pi}{2}out of phases of VR.
  • In L,C circuit, \tt V_{LC}={V_L-V_C} \because VL is π out of phases of VC.
  • In LCR circuit , the total applied voltage (v) across L, C, R is given as \tt V=\sqrt{\left({V_L-V_C}\right)^2+V_R^2}
  • TRANSFORMER is used to transform an alternating voltage from one coil to another
  • A transformer consists two sets of coils, insulated from each other.
  • The coils are wound on a soft iron core, either one on top of the other (or) separate limbs
  • Primary coil has NP turns and the secondary coil has Ns turns.
  • Input is connected across the primary coil where as the output is taken across the secondary coil.
  • When an alternating voltage is applied to the primary, then an emf is induced in secondary.
  • \tt e_{s}=-N_{s}\ \frac{d\phi}{dt} (emf of secondary coil)
  • \tt e_{p}=-N_{p}\ \frac{d\phi}{dt} (emf of primary coil)
  • If the secondary is an open circuit, then eS = VS
    \tt \frac{V_{s}}{V_{p}}=\frac{N_{s}}{N_{p}}=\frac{I_{p}}{I_{s}}
  • \tt \frac{I_{p}}{I_{s}}=\frac{V_{s}}{V_{p}}=\frac{N_{s}}{N_{p}}
    \tt V_{s}=\left(\frac{N_{s}}{N_{p}}\right)V_{p}
  • If NS > NP voltage is stepped up, then the transformer is called STEP-UP TRANSFORMER.
  • If NS < NP voltage is stepped down, then the transformer is called STEP – DOWN TRANSFORMER
  • In step – up transformer VS > VP & IS < IP
  • In step down transformer, VS < VP & IS > IP
  • In step – up transformers primary is made of thick insulated copper wire and secondary is made of thin wire.
  • In step – down transformer primary is made of thin insulated copper wire and secondary is made of a thick wire.
  • \tt Efficiency=\frac{output\ power}{input\ power}
    \tt Percentage\ Efficiency=\frac{output\ power}{input\ power}\times100

AC Voltage Applied to an Inductor View the Topic in this video From 00:18 To 12:28

View the Topic in this video From 00:24 To 9:43

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1. Alternating voltage is applied to the inductor then Alternating emf, E = E0 sin ωt

2. Alternating voltage is applied to the inductor then Alternating current, I = I0 sin (ωt − π/2)

3. Alternating voltage is applied to the inductor then Alternating current lags behind alternating emf by \frac{\pi}{2}

4. Alternating voltage is applied to capacitor then Alternating emf, E = E0 sin ωt

5. Alternating voltage is applied to capacitor then Alternating current, I = I0 sin (ωt + π/2)