NCERT Solutions Class 12 Physics Chapter 7: Alternating Current

Introduction

Chapter 7 of the NCERT Class 12 Physics syllabus delves into Alternating Current (AC), a fundamental topic in the study of electromagnetism and circuits. Understanding AC is crucial as it forms the basis for various applications in modern technology, from household appliances to industrial machinery. This article aims to provide a comprehensive guide to the important questions from this chapter, helping students prepare effectively for their exams.

1. What is Alternating Current (AC)?

Definition and Characteristics:

Alternating Current (AC) is a type of electrical current that periodically reverses direction. Unlike Direct Current (DC), where the flow of electric charge is unidirectional, AC changes its direction periodically. The key characteristics of AC include:

Amplitude: The maximum value of the current or voltage in an AC circuit.
Frequency: The number of cycles the AC waveform completes in one second, measured in Hertz (Hz).
Wavelength: The distance between two consecutive peaks or troughs of the waveform.
Phase: The position of a point in time on a waveform cycle, measured in degrees.

Waveform Representation:

AC can be represented graphically as a sinusoidal waveform, which is the most common form. Other waveforms include triangular and square waves, but sinusoidal waves are predominant in most AC applications.

Mathematical Representation:

The voltage in an AC circuit can be expressed as: $V(t) = V_m \sin(\omega t + \phi)$ where:

$V(t)$ is the instantaneous voltage at time $t$ .
$V_m$ is the maximum (peak) voltage.
$\omega$ is the angular frequency ( $\omega = 2 \pi f$ ).
$\phi$ is the phase angle.

2. Why is AC Preferred Over DC for Power Transmission?

Advantages of AC over DC:

Efficient Transmission: AC can be easily transformed to high voltages using transformers. High-voltage AC transmission reduces energy losses over long distances. DC transmission, on the other hand, is less efficient for long-distance transmission due to higher losses.
Ease of Generation and Distribution: AC generators and motors are simpler and more cost-effective than their DC counterparts. AC can be easily generated and distributed with minimal losses.
Transformers: AC can be easily stepped up or stepped down using transformers. This ability allows for efficient voltage regulation and power distribution.

Historical Context:

The "War of Currents" in the late 19th century between Thomas Edison, who advocated for DC, and Nikola Tesla and George Westinghouse, who promoted AC, highlighted these advantages. AC's ability to be transmitted over long distances made it the dominant choice for electrical power systems.

3. What Are the Key Formulas and Concepts in AC Circuits?

Ohm's Law for AC Circuits:

Ohm's Law in AC circuits is given by: $V = I \cdot Z$ where:

$V$ is the voltage.
$I$ is the current.
$Z$ is the impedance of the circuit.

Impedance (Z):

Impedance is a measure of the opposition that a circuit offers to the flow of alternating current. It is a combination of resistance (R) and reactance (X), and is given by: $Z = \sqrt{R^2 + X^2}$

Reactance (X):

Reactance is the resistance offered by inductors and capacitors to the AC. It has two components:

Inductive Reactance (X_L): $X_L = \omega L$ where $\omega = 2 \pi f$ is the angular frequency and $L$ is the inductance.
Capacitive Reactance (X_C): $X_C = \frac{1}{\omega C}$ where $C$ is the capacitance.

Phase Angle (φ):

The phase angle in an AC circuit is the angle by which the voltage leads or lags the current. It is given by: $\tan \phi = \frac{X}{R}$

Power in AC Circuits:

The power in an AC circuit is divided into three components:

Real Power (P): $P = VI \cos \phi$
Reactive Power (Q): $Q = VI \sin \phi$
Apparent Power (S): $S = VI$

The relationship among these powers is given by: $S^2 = P^2 + Q^2$

4. What Are the Common Types of AC Circuits?

Resistive Circuit:

In a purely resistive AC circuit, the voltage and current are in phase, meaning the phase angle $\phi = 0$ . The impedance is purely resistive, and the power factor is 1.

Inductive Circuit:

In a purely inductive AC circuit, the voltage leads the current by 90 degrees. The impedance is given by the inductive reactance $X_L$ , and the power factor is 0.

Capacitive Circuit:

In a purely capacitive AC circuit, the voltage lags the current by 90 degrees. The impedance is given by the capacitive reactance $X_C$ , and the power factor is 0.

Series R-L Circuit:

In a series R-L circuit, the total impedance is: $Z = \sqrt{R^2 + (\omega L)^2}$ The current lags the voltage by an angle $\phi$ , where $\tan \phi = \frac{\omega L}{R}$ .

Series R-C Circuit:

In a series R-C circuit, the total impedance is: $Z = \sqrt{R^2 + \left(\frac{1}{\omega C}\right)^2}$ The current leads the voltage by an angle $\phi$ , where $\tan \phi = \frac{1}{\omega C R}$ .

Series R-L-C Circuit:

In a series R-L-C circuit, the total impedance is: $Z = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2}$ The phase angle $\phi$ is given by: $\tan \phi = \frac{\omega L - \frac{1}{\omega C}}{R}$

5. What Are Resonance and its Applications?

Resonance in AC Circuits:

Resonance occurs in a series R-L-C circuit when the inductive reactance and capacitive reactance are equal in magnitude: $\omega L = \frac{1}{\omega C}$ At resonance, the impedance of the circuit is purely resistive, and the current is at its maximum value.

Resonant Frequency:

The resonant frequency $f_0$ is given by: $f_0 = \frac{1}{2 \pi \sqrt{LC}}$

Applications of Resonance:

Tuning Circuits: Resonance is used in tuning circuits to select specific frequencies, such as in radio receivers and transmitters.
Filters: Resonant circuits are used in filters to pass or block specific frequency ranges.
Signal Processing: Resonance is employed in signal processing for amplifying certain frequencies and attenuating others.

6. What Are the Practical Implications of AC and AC Circuits?

Power Consumption:

AC circuits are used in various household and industrial applications, such as lighting, heating, and powering appliances. Understanding AC helps in designing efficient power systems and minimizing energy losses.

Transformers:

Transformers, which rely on AC, are crucial for stepping up or stepping down voltage levels in power distribution systems, making long-distance power transmission more efficient.

Electrical Safety:

AC power systems require careful handling and design to ensure safety. Proper insulation, circuit breakers, and grounding are essential to prevent electrical hazards.

Conclusion

Mastering the concepts and solving important questions related to Alternating Current (AC) from Class 12 Physics Chapter 7 is crucial for a solid understanding of both theoretical and practical aspects of electrical circuits. By focusing on definitions, formulas, circuit types, resonance, and practical applications, students can build a strong foundation in AC and excel in their exams. This comprehensive guide serves as a valuable resource for students preparing for their Class 12 Physics examinations and for anyone interested in the field of electrical engineering and physics.

NCERT Solutions Class 12 Physics Chapter 7: Alternating Current - Important Questions