## 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 = i
_{o}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 V
_{C}is \frac{\pi}{2} out of phases of V_{R}. - In L,R circuit, \tt V_{LR}=\sqrt{V_L^2+V_R^2} \because V
_{L}is \frac{\pi}{2}out of phases of V_{R}. - In L,C circuit, \tt V_{LC}={V_L-V_C} \because V
_{L}is π out of phases of V_{C}. - 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 N
_{P}turns and the secondary coil has N_{s}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 e
_{S}= V_{S}

\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 N
_{S}> N_{P}voltage is stepped up, then the transformer is called STEP-UP TRANSFORMER. - If N
_{S}< N_{P}voltage is stepped down, then the transformer is called STEP – DOWN TRANSFORMER - In step – up transformer V
_{S}> V_{P}& I_{S}< I_{P} - In step down transformer, V
_{S}< V_{P}& I_{S}> I_{P} - 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

Disclaimer: Compete.etutor.co may from time to time provide links to third party Internet sites under their respective fair use policy and it may from time to time provide materials from such third parties on this website. These third party sites and any third party materials are provided for viewers convenience and for non-commercial educational purpose only. Compete does not operate or control in any respect any information, products or services available on these third party sites. Compete.etutor.co makes no representations whatsoever concerning the content of these sites and the fact that compete.etutor.co has provided a link to such sites is NOT an endorsement, authorization, sponsorship, or affiliation by compete.etutor.co with respect to such sites, its services, the products displayed, its owners, or its providers.

1. Alternating voltage is applied to the inductor then Alternating emf, *E* = *E*_{0} sin ω*t*

2. Alternating voltage is applied to the inductor then Alternating current, *I* = *I*_{0} sin (ω*t *− 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* = *E*_{0} sin ω*t*

5. Alternating voltage is applied to capacitor then Alternating current, *I* = *I*_{0} sin (ω*t *+ π/2)