Science Notes for Class 12 Alternating Current

Alternating Current (AC)

Welcome to the chapter on Alternating Current (AC) for Class 12. In this chapter, you will learn what alternating current is, how it differs from direct current, the mathematical representation of AC, and its applications in daily life and technology. By the end of this chapter, you will be able to solve problems related to AC circuits and understand the importance of AC in electrical systems.

Introduction

Alternating current (AC) is an electric current that reverses its direction periodically, unlike direct current (DC), which flows only in one direction. Most of the electricity supplied to homes and industries is AC.

Key Concepts

Alternating Current (AC): Current that changes direction and magnitude with time.
Direct Current (DC): Current that flows in one direction only.
Frequency (f): Number of cycles per second, measured in hertz (Hz).
Amplitude (I₀): Maximum value of current or voltage.
Time Period (T): Time taken to complete one cycle (T = 1/f).
Root Mean Square (RMS) Value: Effective value of AC, I_rms = I₀/√2.
Peak Value: The maximum value reached by the AC waveform.

Mathematical Representation of AC

The instantaneous value of alternating current or voltage can be written as:

I(t) = I₀ sin(ωt + φ)
V(t) = V₀ sin(ωt + φ)

where I₀ and V₀ are the peak values, ω is the angular frequency (ω = 2πf), and φ is the phase angle.

AC vs DC

AC changes direction periodically; DC flows in one direction.
AC can be easily transformed to different voltages; DC cannot.
AC is used for power transmission; DC is used in batteries and electronics.

AC Circuit Elements

Resistor (R): Voltage and current are in phase.
Inductor (L): Current lags voltage by 90°.
Capacitor (C): Current leads voltage by 90°.

Impedance and Phase

In AC circuits, impedance (Z) is the total opposition to current and depends on resistance, inductance, and capacitance:

Z = √(R² + (X_L - X_C)²)
X_L = ωL (Inductive reactance)
X_C = 1/(ωC) (Capacitive reactance)

Power in AC Circuits

Instantaneous Power: p(t) = v(t) × i(t)
Average Power: P = V_rms × I_rms × cosφ
Power Factor (cosφ): Ratio of true power to apparent power.

Applications of AC

Electric power transmission and distribution
Household appliances (fans, lights, refrigerators)
Transformers and electric motors

Practice Questions

Define alternating current and give its mathematical expression.
What is the RMS value of an AC current with a peak value of 10 A?
Explain the difference between AC and DC with examples.
Calculate the impedance of a circuit with R = 10 Ω, L = 0.1 H, C = 100 μF, and f = 50 Hz.
Why is AC preferred over DC for long-distance power transmission?

Challenge Yourself

Draw the waveform of AC and DC on the same graph and label them.
A 220 V, 50 Hz AC supply is connected to a 44 Ω resistor. Find the RMS current.

Did You Know?

Nikola Tesla and Thomas Edison had a famous rivalry over AC and DC systems, known as the "War of Currents".
Most countries use 50 Hz or 60 Hz as the standard frequency for AC supply.

Glossary

Alternating Current (AC): Current that reverses direction periodically.
Direct Current (DC): Current that flows in one direction only.
Impedance (Z): Total opposition to AC in a circuit.
RMS Value: Effective value of AC.
Power Factor: Cosine of the phase angle between voltage and current.

Answers to Practice Questions

Alternating current is a current that changes direction and magnitude with time. Its mathematical expression is I(t) = I₀ sin(ωt + φ).
I_rms = I₀/√2 = 10/√2 ≈ 7.07 A
AC changes direction periodically (e.g., household electricity), while DC flows in one direction (e.g., batteries).
ω = 2πf = 2 × 3.14 × 50 = 314 rad/s
X_L = ωL = 314 × 0.1 = 31.4 Ω
X_C = 1/(ωC) = 1/(314 × 100 × 10^-6) ≈ 31.8 Ω
Z = √[10² + (31.4 - 31.8)²] ≈ √[100 + 0.16] ≈ 10.01 Ω
AC can be easily transformed to higher or lower voltages, reducing power loss during transmission.

Understanding AC is essential for modern electrical technology and applications!

Science Class 12 - Alternating Current Notes