Chapter 7 Alternating Current
NCERT Class 12 Physics - Chapter 7: Alternating Current
Introduction to Alternating Current
Alternating Current (AC) is an electric current that reverses its direction periodically. Unlike Direct Current (DC) which flows in a single direction, AC changes direction, typically in a sinusoidal wave pattern. This chapter delves into the fundamental concepts, mathematical descriptions, and applications of alternating current.
7.1 Alternating Current and Voltage
In AC circuits, both the current and voltage vary with time. The most common form of AC is the sinusoidal wave, represented mathematically as:
V(t) = V0 sin(ωt)
where V(t) is the instantaneous voltage, V0 is the peak voltage, ω (omega) is the angular frequency, and t is the time.
7.2 Representation of AC through Phasors
Phasors are a graphical representation of AC quantities like voltage and current. They are rotating vectors that represent the magnitude and phase of sinusoidal functions. The length of the phasor represents the amplitude, and the angle it makes with the reference axis represents the phase angle.
7.3 RMS Value of AC
The Root Mean Square (RMS) value of an AC is a measure of its effective value. For a sinusoidal AC, the RMS value is given by:
Vrms = V0/√2
This value helps in comparing the power of AC with that of DC.
7.4 AC Circuit Containing Pure Resistor
In an AC circuit with a pure resistor, the voltage and current are in phase, meaning they reach their maximum and minimum values simultaneously. The power dissipated in the resistor is given by:
P = Vrms Irms
7.5 AC Circuit Containing Pure Inductor
In a circuit with a pure inductor, the current lags behind the voltage by 90 degrees (π/2 radians). The inductive reactance (XL) is given by:
XL = ωL
where L is the inductance.
7.6 AC Circuit Containing Pure Capacitor
In a circuit with a pure capacitor, the current leads the voltage by 90 degrees. The capacitive reactance (XC) is given by:
XC = 1/(ωC)
where C is the capacitance.
7.7 LCR Series Circuit
An LCR series circuit contains an inductor (L), a capacitor (C), and a resistor (R) in series. The total impedance (Z) of the circuit is given by:
Z = √(R2 + (XL - XC)2)
where XL is the inductive reactance and XC is the capacitive reactance.
7.8 Resonance in AC Circuits
Resonance occurs in an LCR circuit when the inductive reactance equals the capacitive reactance (XL = XC). At resonance, the impedance is minimum, and the circuit behaves like a pure resistor. The resonant frequency (f0) is given by:
f0 = 1/(2π√(LC))
7.9 Power in AC Circuits
The power in an AC circuit is given by the product of the RMS values of voltage and current and the cosine of the phase angle (φ) between them:
P = Vrms Irms cos(φ)
where cos(φ) is the power factor.
7.10 LC Oscillations
LC oscillations occur in a circuit containing an inductor and a capacitor. The energy oscillates between the magnetic field of the inductor and the electric field of the capacitor. The angular frequency (ω) of these oscillations is given by:
ω = 1/√(LC)
7.11 Transformers
Transformers are devices used to increase or decrease AC voltages. They work on the principle of electromagnetic induction. A transformer consists of primary and secondary coils wound on a magnetic core. The voltage transformation ratio is given by:
Vs/Vp = Ns/Np
where Vs and Vp are the secondary and primary voltages, and Ns and Np are the number of turns in the secondary and primary coils, respectively.
Word Meanings
Alternating Current (AC)
An electric current that reverses its direction periodically.
Direct Current (DC)
An electric current flowing in one direction only.
Sinusoidal Wave
A waveform that describes a smooth periodic oscillation.
Phasor
A rotating vector used to represent a sinusoidal function.
RMS Value
The effective value of an alternating current, equal to the value of direct current that would produce the same power dissipation.
Inductive Reactance (XL)
The opposition to the change of current by an inductor in an AC circuit.
Capacitive Reactance (XC)
The opposition to the change of voltage by a capacitor in an AC circuit.
Impedance (Z)
The total opposition to current flow in an AC circuit, comprising both resistance and reactance.
Resonance
The condition in an LCR circuit when the inductive reactance equals the capacitive reactance, resulting in minimum impedance.
Power Factor
The ratio of real power to apparent power in an AC circuit, equal to the cosine of the phase angle between voltage and current.
Transformer
A device used to increase or decrease AC voltages through electromagnetic induction.
LC Oscillations
Oscillations in a circuit containing an inductor and a capacitor, where energy oscillates between the magnetic field of the inductor and the electric field of the capacitor.
FAQs
1. What is alternating current (AC)?
AC is an electric current that reverses its direction periodically, typically in a sinusoidal wave pattern.
2. How is AC different from DC?
DC flows in a single direction, while AC changes direction periodically.
3. What is the RMS value of AC?
The RMS value of AC is the effective value that represents the equivalent DC value that would produce the same power dissipation.
4. What is a phasor?
A phasor is a rotating vector that represents the magnitude and phase of sinusoidal functions in AC circuits.
5. What is the significance of the power factor in AC circuits?
The power factor indicates the efficiency of power usage in an AC circuit, being the ratio of real power to apparent power.
6. What happens in a purely resistive AC circuit?
In a purely resistive AC circuit, the voltage and current are in phase, meaning they reach their peak values simultaneously.
7. What is inductive reactance?
Inductive reactance is the opposition to the change of current by an inductor in an AC circuit.
8. What is capacitive reactance?
Capacitive reactance is the opposition to the change of voltage by a capacitor in an AC circuit.
9. What is the condition for resonance in an LCR circuit?
Resonance occurs when the inductive reactance equals the capacitive reactance, resulting in minimum impedance.
10. How does a transformer work?
A transformer works on the principle of electromagnetic induction to increase or decrease AC voltages.
11. What is the formula for the resonant frequency in an LCR circuit?
The resonant frequency (f0) is given by f0 = 1/(2π√(LC)).
12. What is the relationship between primary and secondary voltages in a transformer?
The relationship is given by Vs/Vp = Ns/Np, where Vs and Vp are the secondary and primary voltages, and Ns and Np are the number of turns in the secondary and primary coils, respectively.
13. What is the angular frequency of LC oscillations?
The angular frequency (ω) is given by ω = 1/√(LC).
14. Why is AC preferred over DC for long-distance power transmission?
AC is preferred because it can be easily transformed to higher or lower voltages, reducing power loss during transmission.
15. What is the role of an inductor in an AC circuit?
An inductor opposes changes in current, causing the current to lag behind the voltage by 90 degrees.
16. What is the role of a capacitor in an AC circuit?
A capacitor opposes changes in voltage, causing the current to lead the voltage by 90 degrees.
17. How is the impedance of an LCR circuit calculated?
Impedance (Z) is calculated as Z = √(R2 + (XL - XC)2).
18. What happens to the power factor at resonance in an LCR circuit?
At resonance, the power factor is 1, indicating maximum power transfer.
19. Can transformers work with DC?
No, transformers require a changing magnetic field to operate, which is not provided by DC.
20. What is the significance of the peak voltage in an AC circuit?
The peak voltage is the maximum voltage reached by the AC waveform, used to calculate the RMS value.