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Class 12 Science (PCM)

Physics Part 1

Alternating Current

Alternating Current

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Study Action Plan (Sorted by Difficulty)
AC Power Transmission Using Transformers
Accuracy: 0%
Total Attempted0
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Difficulty Level:
High
Impedance and Phase Angle in Series LCR Circuit
Accuracy: 0%
Total Attempted2
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Difficulty Level:
High
Power Factor Improvement
Accuracy: 0%
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Difficulty Level:
High
Resonance Frequency and Current Maximisation
Accuracy: 0%
Total Attempted1
Total Correct0
Total Incorrect1
Difficulty Level:
High
AC Voltage Applied to Resistor
Accuracy: 50%
Total Attempted2
Total Correct1
Total Incorrect1
Difficulty Level:
Medium
Transformer Construction and Working
Accuracy: 50%
Total Attempted2
Total Correct1
Total Incorrect1
Difficulty Level:
Medium
Power in AC Circuits
Accuracy: 60%
Total Attempted5
Total Correct3
Total Incorrect2
Difficulty Level:
Medium
Average Power and Heating in Pure Resistor
Accuracy: 67%
Total Attempted3
Total Correct2
Total Incorrect1
Difficulty Level:
Medium
DC and AC Behaviour of Capacitor and Inductor
Accuracy: 67%
Total Attempted3
Total Correct2
Total Incorrect1
Difficulty Level:
Medium
Step-Up and Step-Down Transformers
Accuracy: 67%
Total Attempted3
Total Correct2
Total Incorrect1
Difficulty Level:
Medium
Transformers and Mutual Induction
Accuracy: 67%
Total Attempted3
Total Correct2
Total Incorrect1
Difficulty Level:
Medium
Alternating Current and Voltage
Accuracy: 75%
Total Attempted4
Total Correct3
Total Incorrect1
Difficulty Level:
Low
Series LCR Circuit and Resonance
Accuracy: 80%
Total Attempted5
Total Correct4
Total Incorrect1
Difficulty Level:
Low
AC Voltage Applied to Inductor
Accuracy: 86%
Total Attempted7
Total Correct6
Total Incorrect1
Difficulty Level:
Low
AC Voltage Applied to Capacitor
Accuracy: 100%
Total Attempted2
Total Correct2
Total Incorrect0
Difficulty Level:
Low
Phasor Representation in AC Circuits
Accuracy: 100%
Total Attempted1
Total Correct1
Total Incorrect0
Difficulty Level:
Low
Reactance and Frequency Dependence
Accuracy: 100%
Total Attempted3
Total Correct3
Total Incorrect0
Difficulty Level:
Low
RMS and Peak Values of AC
Accuracy: 100%
Total Attempted2
Total Correct2
Total Incorrect0
Difficulty Level:
Low
Transformer Losses and Efficiency
Accuracy: 100%
Total Attempted1
Total Correct1
Total Incorrect0
Difficulty Level:
Low
Voltage Addition and Phase in AC Circuits
Accuracy: 100%
Total Attempted1
Total Correct1
Total Incorrect0
Difficulty Level:
Low

Learning Objectives

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Learning Objectives

  • Understand the concept of alternating current (AC) and its significance in electrical systems.
  • Describe the characteristics of AC voltage and current, including phase relationships.
  • Explain the operation of inductors and capacitors in AC circuits.
  • Analyze the behavior of series RLC circuits under AC voltage.
  • Calculate the root mean square (rms) values for voltage and current in AC circuits.
  • Define and calculate impedance, reactance, and power factor in AC circuits.
  • Understand the principles of transformers and their applications in voltage transformation.

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Revision Notes & Summary

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Chapter Seven: Alternating Current

7.1 Introduction

  • Direct Current (DC): Currents that do not change direction with time.
  • Alternating Current (AC): Currents that vary with time, commonly represented as a sine function.
  • Importance of AC: Most electrical devices require AC voltage due to its efficient transmission and transformation.

7.2 Key Concepts

  • AC Voltage: Voltage that varies with time, denoted as v = vₘ sin(wt).
  • AC Current: Current driven by AC voltage, denoted as i = iₘ sin(wt + Φ).
  • Peak Values:
    • Peak current: iₘ = √2 * I_rms
    • Peak voltage: vₘ = √2 * V_rms

7.3 Circuit Behavior

  • Inductive Reactance (Xₗ): Xₗ = wL, where w is the angular frequency and L is the inductance.
  • Capacitive Reactance (Xₗ): X_C = 1/(wC), where C is the capacitance.
  • Impedance (Z): Z = √(R² + (Xₗ - X_C)²).
  • Power Factor: cos(Φ) = P/(VI), where P is the average power.

7.4 Transformers

  • Transformer Basics: A device that transforms AC voltage from one level to another using mutual induction.
  • Primary and Secondary Coils:
    • Primary coil (Nₚ turns) connected to AC source.
    • Secondary coil (Nₛ turns) induces voltage based on turns ratio.
  • Voltage Relationship: Vₛ/Vₚ = Nₛ/Nₚ.
  • Current Relationship: Iₛ/Iₚ = Nₚ/Nₛ.

7.5 Example Problem

  • Example 7.5: Inserting an iron rod into an inductor increases inductance, causing the light bulb's glow to decrease due to increased inductive reactance.

7.6 Important Formulas

Physical QuantitySymbolFormulaRemarks
RMS VoltageVV = √2 * vₘAmplitude of AC voltage
RMS CurrentII = √2 * iₘAmplitude of AC current
Inductive ReactanceXₗXₗ = wLDepends on frequency and inductance
Capacitive ReactanceX_CX_C = 1/(wC)Depends on frequency and capacitance
ImpedanceZZ = √(R² + (Xₗ - X_C)²)Total opposition to AC
Power Factor-cos(Φ) = P/(VI)Efficiency of power usage

7.7 Points to Ponder

  1. RMS values are typically used for AC voltage and current measurements.
  2. Average power in AC circuits is calculated using RMS values.
  3. In purely inductive or capacitive circuits, average power is zero despite current flow.
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Practice Test – MCQs, True/False

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Multiple Choice Questions

A.

To convert AC to DC

B.

To change the frequency of AC

C.

To change the voltage level of AC

D.

To store electrical energy
Correct Answer: C

Solution:

A transformer is used to change the voltage level of alternating current (AC) using the principle of mutual induction.

Chapter Concept:

Transformer Construction and Working

A.

The current leads the voltage by π2\frac{\pi}{2} radians.

B.

The current lags the voltage by π2\frac{\pi}{2} radians.

C.

The current is in phase with the voltage.

D.

The current leads the voltage by π\pi radians.
Correct Answer: B

Solution:

In a purely inductive AC circuit, the current lags the voltage by π2\frac{\pi}{2} radians.

Chapter Concept:

Voltage Addition and Phase in AC Circuits

A.

The inductive reactance XLX_L is equal to the capacitive reactance XCX_C.

B.

The impedance ZZ is equal to the resistance RR.

C.

The phase angle is zero.

D.

All of the above.
Correct Answer: D

Solution:

At resonance in a series LCR circuit, XL=XCX_L = X_C, Z=RZ = R, and the phase angle is zero, resulting in maximum current.

Chapter Concept:

Resonance Frequency and Current Maximisation

A.

2.2 A

B.

3.1 A

C.

1.5 A

D.

2.0 A
Correct Answer: A

Solution:

The rms current IrmsI_{rms} in a purely resistive circuit is given by Irms=VrmsR=220100=2.2 AI_{rms} = \frac{V_{rms}}{R} = \frac{220}{100} = 2.2 \text{ A}.

Chapter Concept:

Alternating Current and Voltage

A.

The secondary voltage is higher than the primary voltage.

B.

The secondary current is higher than the primary current.

C.

The number of turns in the secondary coil is greater than in the primary coil.

D.

The power output is greater than the power input.
Correct Answer: B

Solution:

In a step-down transformer, the secondary voltage is less than the primary voltage, but the secondary current is greater than the primary current.

Chapter Concept:

Transformers and Mutual Induction

A.

Zero, because the average AC current is zero.

B.

Non-zero, because heating depends on i2Ri^2R.

C.

Zero, because the resistor does not dissipate power.

D.

Non-zero, because the voltage and current are out of phase.
Correct Answer: B

Solution:

The average power in a resistor is not zero because heating depends on i2Ri^2R, which is always positive.

Chapter Concept:

Average Power and Heating in Pure Resistor

A.

The current amplitude increases.

B.

The current amplitude decreases.

C.

The current amplitude remains the same.

D.

The current amplitude becomes infinite.
Correct Answer: B

Solution:

Beyond the resonant frequency, the impedance of the circuit increases due to the dominance of either capacitive or inductive reactance, resulting in a decrease in current amplitude.

Chapter Concept:

Resonance Frequency and Current Maximisation

A.

π/4\pi/4 radians

B.

π/2\pi/2 radians

C.

π\pi radians

D.

Zero radians
Correct Answer: B

Solution:

In a purely capacitive AC circuit, the current leads the voltage by π/2\pi/2 radians because the capacitive reactance causes a phase shift.

Chapter Concept:

AC Voltage Applied to Capacitor

A.

The impedance is purely resistive.

B.

The current is at its minimum value.

C.

The phase angle between voltage and current is 90 degrees.

D.

The power factor is zero.
Correct Answer: A

Solution:

At resonance in a series LCR circuit, the impedance is purely resistive, meaning the reactances cancel each other out, resulting in the impedance being equal to the resistance (Z=RZ = R).

Chapter Concept:

Resonance Frequency and Current Maximisation

A.

The power factor decreases.

B.

The power factor remains the same.

C.

The power factor increases towards 1.

D.

The power factor becomes zero.
Correct Answer: C

Solution:

Adding a capacitor of appropriate capacitance can improve the power factor by cancelling the lagging wattless component of current, thus increasing the power factor towards 1.

Chapter Concept:

Power Factor Improvement

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Alternating Current

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True or False

Correct Answer: True

Solution:

The impedance formula Z=R2+(XL−XC)2Z = \sqrt{R^2 + (X_L - X_C)^2} correctly represents the effective opposition to AC in a series LCR circuit. The phase angle, determined by the relative magnitudes of XLX_L and XCX_C, indicates if the circuit is inductive (current lags) or capacitive (current leads).

Chapter Concept :

Impedance and Phase Angle in Series LCR Circuit

Correct Answer: False

Solution:

The average power in a resistor is not zero because power depends on i2Ri^2R, which is always positive. Therefore, even though the average AC current over a cycle is zero, the average power is not.

Chapter Concept :

Average Power and Heating in Pure Resistor

Correct Answer: True

Solution:

In a purely inductive circuit, the current lags the voltage by π2\frac{\pi}{2} radians, resulting in the average power over a complete cycle being zero. This is because the instantaneous power, given by p=vip = vi, averages to zero over one cycle due to the phase difference.

Chapter Concept :

AC Voltage Applied to Inductor

Correct Answer: True

Solution:

A capacitor in an AC circuit allows current to flow by continuously charging and discharging with the alternating current. In a DC circuit, once the capacitor is fully charged, it blocks further current flow.

Chapter Concept :

DC and AC Behaviour of Capacitor and Inductor

Correct Answer: True

Solution:

At resonance in a series LCR circuit, XL=XCX_L = X_C, which makes the impedance Z=RZ = R, purely resistive, allowing maximum current to flow.

Chapter Concept :

Series LCR Circuit and Resonance

Correct Answer: False

Solution:

Although the average AC current over a cycle is zero, the average power in a resistor is not zero because heating depends on i2Ri^2R. The average power is given by P=I2R=V2/R=VIP = I^2R = V^2/R = VI using rms values.

Chapter Concept :

Average Power and Heating in Pure Resistor

Correct Answer: False

Solution:

In an AC circuit, the current through a pure capacitor leads the applied voltage by π2\frac{\pi}{2} radians, or 90 degrees. This is due to the capacitive reactance, which causes the current to reach its maximum value before the voltage does.

Chapter Concept :

Alternating Current and Voltage

Correct Answer: True

Solution:

In a purely inductive circuit, the current lags the voltage by π2\frac{\pi}{2} radians or 90 degrees due to the nature of inductive reactance.

Chapter Concept :

AC Voltage Applied to Inductor

Correct Answer: True

Solution:

In a purely inductive circuit, the current lags the voltage by π2\frac{\pi}{2} radians due to the nature of inductive reactance, which causes a phase shift between the voltage and current.

Chapter Concept :

Phasor Representation in AC Circuits

Correct Answer: True

Solution:

In purely inductive or capacitive circuits, the current and voltage are out of phase by π2\frac{\pi}{2}, resulting in a power factor of zero. Therefore, the average power dissipated over a complete cycle is zero.

Chapter Concept :

Power in AC Circuits

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