CBSE Class 12 Physics Notes Chapter 7 Alternating Current

Alternating Current (AC) is a type of electric current that constantly changes polarity and magnitude over time. Imagine water flowing back and forth in a pipe instead of steadily in one direction – that's like AC! Unlike direct current (DC), which always flows in one direction, AC periodically reverses its flow. 

• AC can be easily transformed to high voltages for efficient transmission over long distances, then back to lower voltages for safe home use.
• AC motors are simpler and more efficient than DC motors, making them the workhorses of modern appliances.
• Most electronic devices, from TVs to computers, utilize AC.
• While DC has its own uses, AC's versatility and efficiency make it the dominant form of electricity powering our modern world.
• The frequency of AC (Hz) determines how often it changes direction.
• AC voltage can vary over time, but its effective value is often used for calculations.

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Class 12 Physics Chapter 7 Notes - Alternating Current

Average or Mean Value of AC

• The average or mean value of AC refers to the average value of the voltage or current over a complete cycle.
• It is calculated by integrating the instantaneous values of the waveform over one cycle and dividing by the time period.
• Formula:

I_av = 0.637 I_o

Where

• I_av is the average value of AC
• I_o is the peak value of AC

RMS Value of AC

• It is the amount of steady current which produces the same amount of heat in a certain time interval as is produced by AC during the time period T.
• Formula:

I_rms = 0.707 I_o

Where

• I_rms is the RMS value of AC
• I_o is the peak value of AC

Alternating EMF or Voltage

• Alternating EMF or voltage refers to the voltage that changes direction periodically, typically following a sinusoidal waveform.
• It is commonly represented by V = V_max sin(ωt), where V_max is the maximum voltage, ω is the angular frequency, and t is time.

Inductive Reactance

• Inductive reactance (X_L) is the opposition offered by an inductor to the flow of alternating current.
• It is directly proportional to the frequency of the alternating current and the inductance of the inductor and is given by the formula X_L= 2πf_L.

Capacitive Reactance

• Capacitive reactance (X_C ) is the opposition offered by a capacitor to the flow of alternating current.
• It is inversely proportional to the frequency of the alternating current and the capacitance of the capacitor and is given by the formula X_C = 1/2πf_C.

Representation Of AC Current And Voltage By Rotating Vectors — Phasors

Phasors are rotating vectors used to represent alternating current (AC) voltages and currents graphically.

• They provide a simplified way to visualize the magnitude and phase relationship between AC voltages and currents in sinusoidal circuits.
• The length of the phasor represents the magnitude of the AC quantity, while its angle with respect to a reference axis denotes the phase shift.

AC Voltage Applied To A Resistor

AC voltage applied to a resistor follows Ohm's Law, where the current varies sinusoidally with the applied voltage.

• The current and voltage are in phase in an AC circuit with a resistor. 
• This means they reach their maximum and minimum values simultaneously during each cycle.
• The power dissipated by the resistor in an AC circuit is given by P = V²/R, where V is the root mean square (rms) voltage and R is the resistance. 
• In an AC circuit, both voltage and current vary sinusoidally.
• Instantaneous power also varies sinusoidally over time.
• The effective value, or RMS value, of an AC signal is equivalent to the DC that would produce the same heating effect.
• RMS value is calculated as the square root of the average of the squares of the instantaneous values over one complete cycle.

AC Voltage Applied To An Inductor

In an AC circuit, when voltage is applied to an inductor, the current lags behind the voltage by 90 degrees due to the inductive reactance.

• As the voltage increases or decreases in an AC circuit, the inductor opposes sudden changes by inducing a back EMF, regulating the flow of current.
• An inductor stores energy in its magnetic field during the positive half-cycle of the AC voltage and releases it during the negative half-cycle, maintaining a continuous flow of current.

AC Voltage Applied To A Capacitor

When AC voltage is applied to a capacitor, there is a phase shift between the voltage across the capacitor and the current flowing through it. 

• The current leads the voltage by 90 degrees in a capacitive circuit.
• In an AC circuit, the capacitor alternately charges and discharges as the voltage alternates, storing and releasing electrical energy in each cycle of the AC waveform.
• The impedance of a capacitor in an AC circuit, known as capacitive reactance, is inversely proportional to the frequency of the AC signal. 
• This means that as the frequency increases, the capacitive reactance decreases, allowing more current to flow through the capacitor.

AC Voltage Applied To A Series LCR Circuit

In a series LCR circuit, the applied AC voltage is distributed across the inductor L, capacitor C, and resistor R. 

• Each component experiences a voltage drop or rise depending on the frequency of the applied AC voltage.
• The voltage across the resistor R is in phase with the current, while the voltage across the inductor L leads the current by 90^∘ in a series LCR circuit. 
• Conversely, the voltage across the capacitor C lags behind the current by 90^∘.
• The total impedance of the series LCR circuit is determined by the combination of the inductive reactance X_L, capacitive reactance X_C, and resistive impedance R. 
• Impedance Formula:

Z = √[R² + (X_L – X_C)²]

Resonance

Resonance is a phenomenon where an external force applied to a system matches the natural frequency of the system, resulting in amplified oscillations or vibrations.

• Common examples of resonance include the vibrations of a tuning fork when struck or the swinging of a pendulum at its natural frequency.
• Resonance finds applications in various fields such as music (musical instruments), engineering (bridge construction), and electronics (radio communication), where controlling or harnessing resonance is crucial for optimal performance and efficiency.

Sharpness Of Resonance

The sharpness of resonance refers to how narrow or broad the resonance peak is in a resonance curve.

• It is influenced by the damping factor of a resonant system, where higher damping leads to broader resonance peaks and lower sharpness.
• Sharpness is often quantified by the quality factor (Q-factor), where a higher Q-factor indicates sharper resonance and better energy conservation.

Power In AC Circuit: The Power Factor

The power factor in AC circuits measures the efficiency of power usage and is the ratio of real power (in watts) to apparent power (in volt-amperes).

• It indicates how effectively electrical power is converted into useful work and influences the efficiency of electrical systems and devices.
• The power factor is calculated using the cosine of the phase angle between voltage and current waveforms, where a higher power factor (closer to 1) signifies efficient power usage, while a lower power factor (close to 0) indicates inefficiencies such as reactive power losses.

Power in AC Circuit

• In an AC circuit, power is the rate at which electrical energy is transferred or consumed.
• It consists of two components: real power (P), which is the actual power consumed by the circuit, and reactive power (Q), which represents the power oscillating between the source and load due to reactive elements like inductors and capacitors.

Wattless Current

• Wattless current, also known as reactive current, is the component of current in an AC circuit that flows back and forth between the source and load without performing useful work.
• It is associated with the reactive elements in the circuit, such as inductors and capacitors, and contributes to the reactive power component of the circuit.

LC Oscillations

LC oscillation refers to the oscillatory behaviour in an electrical circuit containing an inductor (L) and a capacitor (C) connected in parallel or series.

• In LC oscillators, energy oscillates between the magnetic field stored in the inductor and the electric field stored in the capacitor, resulting in a continuous cycle of charge and discharge.
• The frequency of LC oscillation is primarily determined by the values of the inductance (L) and capacitance (C) in the circuit, following the formula f = 1/2π√LC.

Transformers

Transformers are electrical devices that transfer electrical energy from one circuit to another through electromagnetic induction.

• They operate on the principle of mutual electromagnetic induction, where changing current in one coil induces a voltage in another coil through a shared magnetic field.
• Transformers are classified into two main types: step-up transformers increase voltage levels, while step-down transformers decrease voltage levels, both maintaining power conservation.

Class 12 Physics Chapter 7 notes are essential for both board exams and competitive tests like NEET and JEE, providing insights into exam patterns and marking schemes. The notes cover AC voltage, alternating current, and circuits involving resistors, inductors, capacitors, and LCR circuits, aiding students in mastering complex concepts. Regular practice of problems based on Chapter 7 helps students develop problem-solving skills and prepares them effectively for board examinations.

There are Some important List Of Top Physics Questions On Alternating Current Asked In CBSE CLASS XII