Class 12 Physics Alternating Current Notes

7.1 Introduction

Alternating current (AC) is an electric current that changes its magnitude and direction periodically. AC is widely used for power distribution because it is easier to transmit over long distances compared to direct current (DC).

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7.2 AC Voltage Applied to a Resistor

• When AC voltage $V = V_0 \sin(\omega t)$V=V0​sin(ωt) is applied to a resistor R, the current through the resistor is:

$$I = \frac{V_0}{R} \sin(\omega t) = I_0 \sin(\omega t)$$I=RV0​​sin(ωt)=I0​sin(ωt)

• Voltage and current are in phase.
• Power consumed:

$$P = I^2 R = I_0^2 R \sin^2(\omega t)$$P=I2R=I02​Rsin2(ωt)

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7.3 Representation of AC Current and Voltage by Rotating Vectors — Phasors

• AC quantities can be represented as rotating vectors (phasors).
• Phasor diagram helps visualize phase relationships between current and voltage in resistors, inductors, and capacitors.
• Key points:
  • Length of phasor = amplitude
  • Angle with reference = phase difference

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7.4 AC Voltage Applied to an Inductor

• When AC voltage is applied across an inductor L:

$$V = L \frac{dI}{dt}$$V=LdtdI​

• Current lags the voltage by 90°.
• Inductive reactance:

$$X_L = \omega L$$XL​=ωL

• Effective current:

$$I = \frac{V_0}{X_L} \sin(\omega t – \frac{\pi}{2})$$I=XL​V0​​sin(ωt−2π​)

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7.5 AC Voltage Applied to a Capacitor

• When AC voltage is applied across a capacitor C:

$$I = C \frac{dV}{dt}$$I=CdtdV​

• Current leads the voltage by 90°.
• Capacitive reactance:

$$X_C = \frac{1}{\omega C}$$XC​=ωC1​

• Effective current:

$$I = \frac{V_0}{X_C} \sin(\omega t + \frac{\pi}{2})$$I=XC​V0​​sin(ωt+2π​)

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7.6 AC Voltage Applied to a Series LCR Circuit

• In a series LCR circuit: R, L, and C are connected in series.
• Impedance (Z):

$$Z = \sqrt{R^2 + (X_L – X_C)^2}$$Z=R2+(XL​−XC​)2​

• Current:

$$I = \frac{V_0}{Z} \sin(\omega t – \phi)$$I=ZV0​​sin(ωt−ϕ)

• Phase angle:

$$\tan \phi = \frac{X_L – X_C}{R}$$tanϕ=RXL​−XC​​

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7.7 Power in AC Circuit: The Power Factor

• Instantaneous power:

$$P = VI = V_0 I_0 \sin(\omega t) \sin(\omega t – \phi)$$P=VI=V0​I0​sin(ωt)sin(ωt−ϕ)

• Average power:

$$P_{\text{avg}} = VI \cos \phi$$Pavg​=VIcosϕ

• Power factor:$\cos \phi$cosϕ
  • Determines how efficiently AC power is used.
  • For purely resistive load: cos φ = 1
  • For purely inductive or capacitive load: cos φ = 0

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7.8 Transformers

• A transformer changes the voltage of AC using electromagnetic induction.
• Primary coil receives input voltage, secondary coil delivers output voltage.
• Voltage relation:

$$\frac{V_s}{V_p} = \frac{N_s}{N_p}$$Vp​Vs​​=Np​Ns​​

• Current relation:

$$\frac{I_s}{I_p} = \frac{N_p}{N_s}$$Ip​Is​​=Ns​Np​​

• Transformers are essential for power transmission to reduce energy loss.