 # 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
Circuit is predominantly Inductive
• If \tt \frac{1}{\omega c} > {L\omega} ; φ is negative
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

### 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)