ROUTERA

Alternating Current

Class 12th Physics Chapter Case Study

Case Study 1: Understanding Alternating Current (AC)

Alternating current (AC) is an electric current that periodically reverses direction, unlike direct current (DC), which flows in one direction. The most common form of AC is sinusoidal, characterized by its peak voltage and frequency. AC is widely used in households and industries due to its efficiency in power transmission over long distances.

Questions:

  1. What is the primary advantage of using alternating current over direct current for power distribution?
    • a) AC can be easily converted to different voltage levels.
    • b) AC is safer than DC.
    • c) AC does not require transformers.
    • d) AC has lower resistance.
  2. The standard frequency of AC in India is:
    • a) 25 Hz
    • b) 50 Hz
    • c) 60 Hz
    • d) 100 Hz
  3. In a sinusoidal AC wave, the maximum value of voltage is called:
    • a) RMS voltage
    • b) Peak voltage
    • c) Average voltage
    • d) Effective voltage
  4. The time taken to complete one full cycle of an AC wave is known as:
    • a) Frequency
    • b) Period
    • c) Amplitude
    • d) Wavelength

Answers:

  1. a) AC can be easily converted to different voltage levels.
  2. b) 50 Hz
  3. b) Peak voltage
  4. b) Period

Case Study 2: RMS and Average Value of AC

The root mean square (RMS) value of an AC voltage is the effective value, which produces the same amount of heat in a resistor as a corresponding direct current (DC). The average value of AC over one complete cycle is zero; however, the average of the absolute value can be calculated, which is useful in practical applications.

Questions:

  1. The RMS value of an AC voltage is defined as:
    • a) The peak value divided by √2
    • b) The average value multiplied by 2
    • c) The effective value of AC that produces the same heat as DC
    • d) The peak value times √2
  2. For a sinusoidal wave, the relationship between the peak voltage (V₀) and RMS voltage (V_rms) is given by:
    • a) V_rms = V₀/2
    • b) V_rms = V₀√2
    • c) V_rms = V₀/√2
    • d) V_rms = 2V₀
  3. The average value of a sinusoidal AC wave over one complete cycle is:
    • a) V₀
    • b) V_rms
    • c) Zero
    • d) V₀/2
  4. In practical applications, the RMS value is used because:
    • a) It is easier to measure.
    • b) It is always higher than the peak value.
    • c) It corresponds to the power consumed.
    • d) It is independent of frequency.

Answers:

  1. c) The effective value of AC that produces the same heat as DC
  2. c) V_rms = V₀/√2
  3. c) Zero
  4. c) It corresponds to the power consumed.

Case Study 3: AC Circuits and Impedance

In AC circuits, impedance (Z) is the total opposition to the flow of alternating current. It combines resistance (R), inductive reactance (X_L), and capacitive reactance (X_C). The behavior of AC circuits varies with frequency, as inductors and capacitors react differently compared to resistors.

Questions:

  1. Impedance in an AC circuit is defined as:
    • a) The ratio of voltage to current
    • b) The square root of the sum of squares of resistance and reactance
    • c) The total resistance only
    • d) The difference between inductance and capacitance
  2. In a purely resistive AC circuit, the impedance is equal to:
    • a) Zero
    • b) The inductive reactance
    • c) The resistive component
    • d) The capacitive reactance
  3. The relationship between voltage (V), current (I), and impedance (Z) in an AC circuit is given by:
    • a) V = I/Z
    • b) V = IZ
    • c) V = I + Z
    • d) V = I - Z
  4. The phase difference between voltage and current in an inductor is:
    • a) 0 degrees
    • b) 90 degrees
    • c) 180 degrees
    • d) 270 degrees

Answers:

  1. b) The square root of the sum of squares of resistance and reactance
  2. c) The resistive component
  3. a) V = I/Z
  4. b) 90 degrees

Case Study 4: Resonance in AC Circuits

Resonance occurs in an AC circuit when the inductive reactance (X_L) and capacitive reactance (X_C) are equal. At this point, the impedance is minimized, leading to maximum current flow. Resonant circuits are used in applications like radio transmitters and receivers.

Questions:

  1. Resonance in an RLC circuit occurs when:
    • a) X_L > X_C
    • b) X_L < X_C
    • c) X_L = X_C
    • d) R = 0
  2. At resonance, the impedance of the circuit is:
    • a) Maximum
    • b) Minimum
    • c) Equal to the inductive reactance
    • d) Equal to the capacitive reactance
  3. The frequency at which resonance occurs in an RLC circuit is called:
    • a) Cut-off frequency
    • b) Critical frequency
    • c) Resonant frequency
    • d) Natural frequency
  4. Which of the following applications commonly uses resonant circuits?
    • a) Electric heaters
    • b) Radio broadcasting
    • c) DC motors
    • d) Light bulbs

Answers:

  1. c) X_L = X_C
  2. b) Minimum
  3. c) Resonant frequency
  4. b) Radio broadcasting

Case Study 5: Power in AC Circuits

In AC circuits, power is categorized into active power (real power), reactive power, and apparent power. The active power is the power consumed by resistive components, while reactive power is associated with inductors and capacitors. The apparent power is the product of the RMS voltage and RMS current.

Questions:

  1. Active power (P) in an AC circuit is measured in:
    • a) Volt-Amperes
    • b) Watts
    • c) Reactive Volt-Amperes
    • d) Ohms
  2. The formula for apparent power (S) in an AC circuit is:
    • a) S = P + Q
    • b) S = VI
    • c) S = P^2 + Q^2
    • d) S = P - Q
  3. Which of the following correctly defines reactive power (Q)?
    • a) Power consumed by resistors
    • b) Power stored in the electric field of capacitors
    • c) Power that is returned to the source
    • d) Power converted into useful work
  4. The power factor (PF) in an AC circuit is defined as:
    • a) PF = P/S
    • b) PF = Q/S
    • c) PF = S/P
    • d) PF = P/Q

Answers:

  1. b) Watts
  2. b) S = VI
  3. c) Power that is returned to the source
  4. a) PF = P/S