Electricity plays a vital role in our daily lives, and its two main forms are Direct Current (DC) and Alternating Current (AC). While DC flows in a single direction, AC changes its direction periodically. Alternating Current is the backbone of modern power systems because it is easier to transmit over long distances, can be transformed to different voltage levels, and is widely used in industries and homes.
In Class 12 Physics, the chapter Alternating Current covers the fundamental concepts, mathematical analysis, and applications of AC circuits. It is an important topic from both the examination and competitive exam point of view.
In this article, we will cover:
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Basics of Alternating Current
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Mathematical Representation
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AC Circuit Components
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Phasor Diagrams
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Important Formulas and Derivations
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Power in AC Circuits
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Resonance, Transformers, and Applications
Class 12 Physics Alternating Current Notes | Complete Syllabus, Formulas & Questions
What is Alternating Current?
Alternating Current (AC) is defined as the current whose magnitude and direction change periodically with time.
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In simple words, it keeps oscillating back and forth instead of flowing in one direction like DC.
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The most common waveform of AC is a sinusoidal wave.
Mathematically, alternating current can be represented as:
i(t)=I0sin(ωt+ϕ)i(t) = I_0 \sin(\omega t + \phi)
Where:
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i(t)i(t) = Instantaneous current at time t
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I0I_0 = Peak current or maximum current
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ω\omega = Angular frequency (2πf)(2 \pi f)
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ff = Frequency of AC
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ϕ\phi = Phase constant
Difference Between AC and DC
| Feature | Direct Current (DC) | Alternating Current (AC) |
|---|---|---|
| Direction | Flows in one direction only | Changes direction periodically |
| Source | Batteries, Solar Cells | Generators, Power Stations |
| Transmission | Limited distance | Long-distance transmission easy |
| Voltage Control | Difficult | Easy with transformers |
| Example | Electric vehicles | Household electricity supply |
Mathematical Representation of AC
Instantaneous Value
The value of current or voltage at any instant of time is called the instantaneous value.
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i=I0sin(ωt)i = I_0 \sin(\omega t)
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v=V0sin(ωt)v = V_0 \sin(\omega t)
Peak Value
The maximum value of current or voltage in the cycle is called the peak value.
I0=Maximum current,V0=Maximum voltageI_0 = \text{Maximum current}, \quad V_0 = \text{Maximum voltage}
Root Mean Square (RMS) Value
RMS value is the effective value of AC, defined as:
Irms=I02,Vrms=V02I_{rms} = \frac{I_0}{\sqrt{2}}, \quad V_{rms} = \frac{V_0}{\sqrt{2}}
Phasor Representation of AC
AC quantities are often represented using phasors for easy analysis. A phasor is a rotating vector that represents the magnitude and phase of a sinusoidal wave.
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The length of the phasor = Peak value
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Angle with respect to the reference axis = Phase
AC Through Circuit Elements
1. AC Through Pure Resistor
If AC passes through a pure resistor:
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Current and voltage are in phase.
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The relation is V=IRV = IR.
Power consumed:
P=Vrms×Irms×cosϕwhere ϕ=0∘P = V_{rms} \times I_{rms} \times \cos\phi \quad \text{where} \ \phi = 0^\circ
2. AC Through Pure Inductor
If AC passes through an inductor:
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Current lags behind voltage by 90∘90^\circ.
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Inductive reactance:
XL=ωL=2πfLX_L = \omega L = 2 \pi f L
Where L = Inductance
3. AC Through Pure Capacitor
If AC passes through a capacitor:
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Current leads voltage by 90∘90^\circ.
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Capacitive reactance:
XC=1ωC=12πfCX_C = \frac{1}{\omega C} = \frac{1}{2 \pi f C}
Where C = Capacitance
4. AC Through Series LCR Circuit
When a resistor (R), inductor (L), and capacitor (C) are connected in series with AC supply:
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Impedance Z=R2+(XL−XC)2Z = \sqrt{R^2 + (X_L – X_C)^2}
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Current I=VZI = \frac{V}{Z}
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Phase difference ϕ=tan−1(XL−XCR)\phi = \tan^{-1} \left( \frac{X_L – X_C}{R} \right)
Resonance in LCR Circuit
When inductive reactance XLX_L = Capacitive reactance XCX_C:
XL=XC⇒ωL=1ωCX_L = X_C \quad \Rightarrow \quad \omega L = \frac{1}{\omega C}
The circuit impedance becomes minimum, and current becomes maximum. This condition is called resonance.
Resonant frequency:
fr=12πLCf_r = \frac{1}{2 \pi \sqrt{LC}}
Power in AC Circuits
Power Factor
cosϕ=True PowerApparent Power\cos \phi = \frac{\text{True Power}}{\text{Apparent Power}}
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True Power (P) = VrmsIrmscosϕV_{rms} I_{rms} \cos \phi
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Apparent Power = VrmsIrmsV_{rms} I_{rms}
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Reactive Power = VrmsIrmssinϕV_{rms} I_{rms} \sin \phi
Transformers
Transformers work on the principle of mutual induction and are used to step up or step down AC voltage.
VsVp=NsNp\frac{V_s}{V_p} = \frac{N_s}{N_p}
Where Vs,VpV_s, V_p = Secondary and primary voltages, Ns,NpN_s, N_p = Number of turns
Advantages of AC Over DC
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Easy voltage transformation
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Less energy loss during transmission
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Can be transmitted over long distances
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Maintenance cost is low
Important Formulas in AC
| Quantity | Formula |
|---|---|
| RMS Current | Irms=I02I_{rms} = \frac{I_0}{\sqrt{2}} |
| RMS Voltage | Vrms=V02V_{rms} = \frac{V_0}{\sqrt{2}} |
| Impedance | Z=R2+(XL−XC)2Z = \sqrt{R^2 + (X_L – X_C)^2} |
| Resonant Frequency | fr=12πLCf_r = \frac{1}{2 \pi \sqrt{LC}} |
| Power Factor | cosϕ=RZ\cos \phi = \frac{R}{Z} |
| Inductive Reactance | XL=ωLX_L = \omega L |
| Capacitive Reactance | XC=1ωCX_C = \frac{1}{\omega C} |
Objective Questions (MCQs)
Q1: The frequency of AC used in India is:
(a) 50 Hz
(b) 60 Hz
(c) 100 Hz
(d) 25 Hz
Answer: (a) 50 Hz
Q2: At resonance, impedance in LCR circuit is:
(a) Maximum
(b) Minimum
(c) Zero
(d) Infinite
Answer: (b) Minimum
Q3: In a pure capacitor, current:
(a) Leads voltage
(b) Lags voltage
(c) In phase with voltage
(d) None of these
Answer: (a) Leads voltage
Q4: Power factor of pure inductor is:
(a) 1
(b) 0
(c) -1
(d) 0.5
Answer: (b) 0
Q5: RMS value of AC is equal to:
(a) I0I_0
(b) I02\frac{I_0}{\sqrt{2}}
(c) 2I02I_0
(d) 2I0\sqrt{2} I_0
Answer: (b) I02\frac{I_0}{\sqrt{2}}
Q6. At resonance in an LCR circuit, the impedance is:
(a) Zero
(b) Maximum
(c) Minimum
(d) Infinite
Answer: (c) Minimum
Q7. In a purely capacitive circuit, current leads voltage by:
(a) 45∘45^\circ
(b) 60∘60^\circ
(c) 90∘90^\circ
(d) 0∘0^\circ
Answer: (c) 90∘90^\circ
Q8. The unit of inductive reactance is:
(a) Ohm
(b) Farad
(c) Henry
(d) Tesla
Answer: (a) Ohm
Q9. The power factor in a pure resistive circuit is:
(a) 0
(b) 1
(c) -1
(d) 12\frac{1}{\sqrt{2}}
Answer: (b) 1
Q10. A transformer works on the principle of:
(a) Self-induction
(b) Mutual induction
(c) Electromagnetic force
(d) Static electricity
Answer: (b) Mutual induction
Q11. Inductive reactance increases with:
(a) Decrease in frequency
(b) Increase in frequency
(c) Constant frequency
(d) Resistance
Answer: (b) Increase in frequency
Q12. In an AC circuit, power consumed is given by:
(a) VIV I
(b) VIcosϕV I \cos\phi
(c) VIsinϕV I \sin\phi
(d) VI2V I^2
Answer: (b) VIcosϕV I \cos\phi
Q13. The current through a pure inductor:
(a) Leads the voltage
(b) Lags the voltage
(c) In phase with voltage
(d) None of these
Answer: (b) Lags the voltage
Q14. The unit of power factor is:
(a) Watt
(b) Joule
(c) No unit
(d) Volt
Answer: (c) No unit
Q15. The maximum value of current in AC is called:
(a) RMS value
(b) Peak value
(c) Average value
(d) Instantaneous value
Answer: (b) Peak value
Q16. Which of the following circuits has zero power factor?
(a) Resistive circuit
(b) Inductive circuit
(c) Capacitive circuit
(d) Inductive or Capacitive circuit alone
Answer: (d) Inductive or Capacitive circuit alone
Q17. The formula for resonant frequency in an LCR circuit is:
(a) f=1LCf = \frac{1}{LC}
(b) f=12πLCf = \frac{1}{2\pi \sqrt{LC}}
(c) f=LCf = \sqrt{LC}
(d) f=2πLCf = 2\pi LC
Answer: (b) f=12πLCf = \frac{1}{2\pi \sqrt{LC}}
Q18. Which device converts AC to DC?
(a) Transformer
(b) Rectifier
(c) Oscillator
(d) Amplifier
Answer: (b) Rectifier
Q19. The effective value of AC is also known as:
(a) Peak value
(b) RMS value
(c) Instantaneous value
(d) Maximum value
Answer: (b) RMS value
Q20. The phase difference between voltage and current in a pure capacitor is:
(a) 0∘0^\circ
(b) 90∘90^\circ
(c) 180∘180^\circ
(d) 45∘45^\circ
Answer: (b) 90∘90^\circ
Short Answer Questions (5)
Q1: Define Alternating Current (AC).
Answer: Alternating Current (AC) is an electric current whose magnitude and direction change periodically with time. The most common form of AC is sinusoidal, represented mathematically as i=I0sin(ωt+ϕ)i = I_0 \sin(\omega t + \phi).
Q2: What is RMS value of AC?
Answer: The RMS (Root Mean Square) value of AC is the effective value that produces the same power as a DC current of the same magnitude. It is given by Irms=I02I_{rms} = \frac{I_0}{\sqrt{2}} for current and Vrms=V02V_{rms} = \frac{V_0}{\sqrt{2}} for voltage.
Q3: What is the phase difference in a pure inductor circuit?
Answer: In a pure inductor circuit, the current lags the voltage by 90∘90^\circ. This means voltage reaches its peak value earlier than current.
Q4: Write the formula for resonance frequency in an LCR circuit.
Answer: The resonance frequency of an LCR circuit is given by:
fr=12πLCf_r = \frac{1}{2\pi\sqrt{LC}}
where LL is inductance and CC is capacitance.
Q5: What is power factor in AC circuits?
Answer: The power factor is the cosine of the phase angle between voltage and current in an AC circuit. It is given by cosϕ=RZ\cos \phi = \frac{R}{Z}. A higher power factor means more efficient power usage.
Long Answer Questions (5)
Q1: Explain the difference between AC and DC with examples.
Answer: AC (Alternating Current) changes its direction and magnitude periodically, whereas DC (Direct Current) flows in one direction only. AC is represented as a sinusoidal waveform and used in household electricity supply, while DC comes from batteries and solar cells. AC is easy to transmit over long distances with minimal power loss using transformers, whereas DC is limited to short distances due to voltage drop issues.
Q2: Derive the expression for current in a series LCR circuit.
Answer: In a series LCR circuit, the total impedance ZZ is given by Z=R2+(XL−XC)2Z = \sqrt{R^2 + (X_L – X_C)^2}, where XL=ωLX_L = \omega L and XC=1ωCX_C = \frac{1}{\omega C}. Using Ohm’s law, the current is I=VZI = \frac{V}{Z}. The phase difference between voltage and current is ϕ=tan−1(XL−XCR)\phi = \tan^{-1}\left(\frac{X_L – X_C}{R}\right). When XL=XCX_L = X_C, the impedance is minimum, and the circuit is said to be at resonance.
Q3: Explain power in AC circuits with the formula.
Answer: In AC circuits, power consumed is given by P=VrmsIrmscosϕP = V_{rms} I_{rms} \cos \phi, where cosϕ\cos \phi is the power factor.
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True power = VrmsIrmscosϕV_{rms} I_{rms} \cos \phi
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Reactive power = VrmsIrmssinϕV_{rms} I_{rms} \sin \phi
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Apparent power = VrmsIrmsV_{rms} I_{rms}
The power factor indicates the efficiency of power usage.
Q4: What is resonance in an AC circuit? Explain its significance.
Answer: Resonance in an LCR circuit occurs when the inductive reactance XLX_L equals the capacitive reactance XCX_C, i.e., XL=XCX_L = X_C. At this condition, the impedance becomes minimum, and the current reaches its maximum value. Resonance is used in radio receivers, transmitters, and various communication systems to select desired frequencies.
Q5: Discuss the working principle of a transformer.
Answer: A transformer works on the principle of mutual induction. It has two coils – primary and secondary – wound on a magnetic core. When alternating current flows through the primary coil, it produces a changing magnetic flux that induces an EMF in the secondary coil. The voltage transformation ratio is given by VsVp=NsNp\frac{V_s}{V_p} = \frac{N_s}{N_p}, where NsN_s and NpN_p are the number of turns in the secondary and primary coils.
FAQs on Alternating Current
Q1: What is the main advantage of AC over DC?
Answer: AC can be transmitted over long distances with less power loss and can be easily transformed to different voltage levels.
Q2: What is the phase difference between current and voltage in a pure resistor?
Answer: In a pure resistor, current and voltage are in phase.
Q3: What is resonance in AC circuits?
Answer: Resonance occurs when inductive reactance equals capacitive reactance, and circuit impedance is minimum.
Q4: What is the RMS value of a sinusoidal AC?
Answer: Irms=I02I_{rms} = \frac{I_0}{\sqrt{2}}
Q5: Why are phasor diagrams used in AC circuits?
Answer: Phasor diagrams represent the magnitude and phase relationship between voltage and current graphically, making analysis easy.
Conclusion
The study of Alternating Current is essential for understanding modern power systems and electronic circuits. From basics to resonance and power factor, every concept has practical importance in real-life electrical systems. For Class 12 Physics students, mastering this chapter ensures strong fundamentals for board exams and competitive exams like JEE and NEET.