CUET UG Physics Booster Test 3-Foundations of Alternating Current
📌 Answers are locked once submitted — results and explanations appear at the end.
QUESTION 1 OF 20
The shape of an alternating mains voltage over time and its average value over a full cycle:
QUESTION 2 OF 20
Match List I with List II regarding AC quantities:
| List I | List II |
|---|---|
| 1. AC Voltage | a. Zero over one cycle |
| 2. AC Current | b. vm sin(ωt) |
| 3. Average current | c. i²R |
| 4. Instantaneous power | d. im sin(ωt) |
QUESTION 3 OF 20
A light bulb has a resistance of 484 Ω and operates directly on a 220 V rms ac supply. What is the average power consumed by the bulb over a complete cycle?
QUESTION 4 OF 20
In a purely inductive circuit driven by an instantaneous voltage v = vm sin(ωt),
QUESTION 5 OF 20
The voltage amplitude in an AC circuit is,
1. is symbolically denoted by vm
2. is exactly equal to the rms voltage multiplied by 1.414
3. is strictly independent of the rms current
4. represents the peak value of the oscillating potential difference
Choose the correct option:
QUESTION 6 OF 20
Consider the statements regarding current amplitude in a pure resistor. Choose the correct statements.
1. It is analytically calculated by dividing voltage amplitude by resistance
2. It is computationally equal to the rms current divided by 0.707
3. It predictably reaches its maximum value exactly when the voltage reaches its minimum
4. It actively determines the peak instantaneous power along with voltage amplitude
QUESTION 7 OF 20
Identify the incorrect statement about the effective or rms voltage:
QUESTION 8 OF 20
Identify the correct statements about the calculation of peak values from RMS:
1. The peak voltage is invariably larger than the rms voltage by a factor of √2
2. A 220 V rms supply yields a peak voltage of approximately 311 V
3. The established relation holds reliably true for purely sinusoidal voltages
4. Peak voltage is mathematically smaller than rms voltage
QUESTION 9 OF 20
The value of the integration of sin²(ωt) over one complete cycle divided by the period T, which is structurally used to derive the RMS current, is calculated precisely to:
QUESTION 10 OF 20
If an alternating current has a peak value of 1.414 A, what is the equivalent DC current that would produce the identical average Joule heating in a given resistor?
QUESTION 11 OF 20
Consider the statements regarding rotating vector (phasor) analysis. Choose the correct statements.
1. Phasors rotate counter-clockwise with an angular frequency ω
2. The length of the phasor is explicitly proportional to the rms or peak value of the alternating quantity
3. Phasors adeptly represent scalar physical quantities mathematically
4. Phasors strictly represent physical vectors navigating in 3D space
QUESTION 12 OF 20
Choose the correct statements about the projection of phasors:
1. The vertical projection of the voltage phasor distinctly represents vm sin(ωt)
2. The projection gives the tangible value of the voltage at that specific instant
3. As the phasor physically rotates, the projection effectively generates a sinusoidal curve
4. The vertical component remains strictly constant over progressing time
QUESTION 13 OF 20
Choose the incorrect statement about angular frequency and frequency:
QUESTION 14 OF 20
Regarding the specific phase angle between voltage and current in basic AC circuits:
1. In a pure resistor, the phase angle is exactly zero
2. In a pure inductor, the current consistently lags the voltage by π/2
3. In a pure capacitor, the current predictably leads the voltage by π/2
4. The phase angle primarily dictates the amount of wattless current
Choose correct:
QUESTION 15 OF 20
Which of the following was explicitly NOT mentioned as a defining invention or conception of Nikola Tesla?
QUESTION 16 OF 20
The primary electrical systems advocated enthusiastically by George Westinghouse and Thomas Edison respectively were:
QUESTION 17 OF 20
Match List I with List II regarding transformers and power transmission:
| List I | List II |
|---|---|
| 1. Step-up transformer | a. Output coil |
| 2. Step-down transformer | b. Reduces voltage |
| 3. Primary coil | c. Increases voltage |
| 4. Secondary coil | d. Input coil |
QUESTION 18 OF 20
In an AC distribution network, when electrical energy is transmitted economically over long distances,
QUESTION 19 OF 20
Choose the correct statements about AC voltage applied to a pure resistor:
1. The voltage and current are exactly in phase with each other
2. The minima, zero, and maxima of voltage and current naturally occur at the same respective times
3. Ohm's law fundamentally works equally well for AC and DC voltages in resistors
4. The average power dissipated predictably averages to zero
QUESTION 20 OF 20
Identify the incorrect statement about the measurable current passing through a pure resistor in an AC circuit:
Test Complete!
Answer Review
1 The shape of an alternating mains voltage over time and its average value over a full cycle:
�� AC mains voltage varies sinusoidally with time. �� Positive and negative halves are equal and opposite. �� Average value over one complete cycle is zero.
The alternating mains voltage is represented by a sinusoidal function: v = vm sin(ωt) Therefore, the shape of the waveform is sinusoidal. During one complete cycle, the positive half-cycle and negative half-cycle cancel each other exactly. Hence the average value of the voltage over a complete cycle is zero. Thus, "Sine function, Zero" is the correct combination.
- �� Option B → The waveform is sinusoidal, but the average value is not maximum; it is zero.
- �� Option C → AC voltage is not constant; it changes continuously with time.
- �� Option D → AC voltage does not follow a tangent function and its average value is not minimum.
Used
- Elimination
Application:
- Eliminate options that contradict the standard sinusoidal nature of AC voltage.
Final Logic:
- AC voltage is sinusoidal and has zero average value over a complete cycle.
AC = Sine Wave + Zero Average
2 Match List I with List II regarding AC quantities:
| List I | List II |
|---|---|
| 1. AC Voltage | a. Zero over one cycle |
| 2. AC Current | b. vm sin(ωt) |
| 3. Average current | c. i²R |
| 4. Instantaneous power | d. im sin(ωt) |
�� AC voltage = vm sin(ωt) �� AC current = im sin(ωt) �� Average current over a cycle = 0 �� Instantaneous power = i²R
1 → b because AC voltage is represented as vm sin(ωt). 2 → d because AC current is represented as im sin(ωt). 3 → a because the average current over a complete cycle is zero. 4 → c because instantaneous power dissipated in a resistor is i²R. Hence: 1-b, 2-d, 3-a, 4-c
- �� Option B → AC voltage and AC current expressions are interchanged.
- �� Option C → Average current and current expression are incorrectly matched.
- �� Option D → Power and voltage expressions are mismatched.
Used
- Option Grouping
Application:
- Match standard AC expressions with their corresponding quantities.
Final Logic:
- Only Option A provides all correct pairings.
Voltage–Current–Average–Power = V–I–Zero–i²R
3 A light bulb has a resistance of 484 Ω and operates directly on a 220 V rms ac supply. What is the average power consumed by the bulb over a complete cycle?
�� RMS values are used in AC power calculations. �� Average power in a resistor is P = V²/R. �� Use RMS voltage directly.
Given: Vrms = 220 V R = 484 Ω Average power: P = V²/R P = (220)²/484 P = 48400/484 P = 100 W Therefore, the average power consumed by the bulb is 100 W.
- �� Option A → Obtained from incorrect substitution.
- �� Option C → Confuses resistance value with power.
- �� Option D → Approximately equal to peak voltage, not power.
Used
- Substitution
Application:
- Apply the average power formula using given RMS voltage and resistance.
Final Logic:
- P = 220²/484 = 100 W.
Power = V²/R
4 In a purely inductive circuit driven by an instantaneous voltage v = vm sin(ωt),
�� AC current oscillates about zero. �� No DC component exists. �� Integration constant becomes zero.
For a pure inductor: v = L(di/dt) Integrating introduces a constant of integration. Since the current in an AC circuit oscillates equally above and below zero and contains no steady DC component, the integration constant must be zero. Hence Option A is correct.
- �� Option B → No steady direct current exists in the circuit.
- �� Option C → di/dt varies continuously with time.
- �� Option D → Voltage explicitly depends on time through sin(ωt).
Used
- Elimination
Application:
- Reject statements inconsistent with sinusoidal AC behavior.
Final Logic:
- The absence of a DC component makes the integration constant zero.
Pure AC → No DC Offset
5 The voltage amplitude in an AC circuit is,
1. is symbolically denoted by vm
2. is exactly equal to the rms voltage multiplied by 1.414
3. is strictly independent of the rms current
4. represents the peak value of the oscillating potential difference
Choose the correct option:
�� vm denotes peak voltage. �� Vm = √2 Vrms. �� Amplitude means maximum value.
1. Correct — vm is the symbol for voltage amplitude. 2. Correct — Vm = √2Vrms ≈ 1.414Vrms. 3. Incorrect — In a resistive circuit, RMS current depends on voltage amplitude through Ohm's law. 4. Correct — Amplitude represents the maximum value of the oscillating voltage. Hence statements 1, 2 and 4 are correct.
- �� Option A → Includes incorrect statement 3.
- �� Option C → Includes incorrect statement 3.
- �� Option D → Includes incorrect statement 3.
Used
- Elimination
Application:
- Evaluate each statement using RMS relations and Ohm's law.
Final Logic:
- Only statement 3 is incorrect.
Amplitude = Peak = 1.414 × RMS
6 Consider the statements regarding current amplitude in a pure resistor. Choose the correct statements.
1. It is analytically calculated by dividing voltage amplitude by resistance
2. It is computationally equal to the rms current divided by 0.707
3. It predictably reaches its maximum value exactly when the voltage reaches its minimum
4. It actively determines the peak instantaneous power along with voltage amplitude
�� im = vm/R �� im = Irms/0.707 �� Peak power depends on peak voltage and current.
1. Correct — From Ohm's law, im = vm/R. 2. Correct — Since Irms = im/√2, im = Irms/0.707. 3. Incorrect — In a pure resistor, voltage and current are in phase and reach maxima simultaneously. 4. Correct — Instantaneous power depends on both voltage and current amplitudes. Thus statements 1, 2 and 4 are correct.
- �� Option B → Includes incorrect statement 3.
- �� Option C → Includes incorrect statement 3.
- �� Option D → Includes incorrect statement 3.
Used
- Elimination
Application:
- Use phase relationships in a pure resistor.
Final Logic:
- Statement 3 contradicts the in-phase nature of voltage and current.
Resistor → V and I Peak Together
7 Identify the incorrect statement about the effective or rms voltage:
�� Household voltage is RMS voltage. �� Vrms = Vm/√2. �� RMS values simplify power calculations.
Domestic supply voltage ratings such as 220 V refer to RMS values, not peak values. Peak voltage: Vm = √2 × 220 ≈ 311 V Therefore statement C is incorrect.
- �� Option A → Correct statement regarding AC power.
- �� Option B → Correct RMS relation.
- �� Option D → Correct for a resistive circuit.
Used
- Odd One Out
Application:
- Identify the statement inconsistent with RMS voltage definitions.
Final Logic:
- 220 V is an RMS value, not a peak value.
Home Voltage = RMS Voltage
8 Identify the correct statements about the calculation of peak values from RMS:
1. The peak voltage is invariably larger than the rms voltage by a factor of √2
2. A 220 V rms supply yields a peak voltage of approximately 311 V
3. The established relation holds reliably true for purely sinusoidal voltages
4. Peak voltage is mathematically smaller than rms voltage
�� Vm = √2Vrms. �� 220 V RMS gives 311 V peak. �� Formula applies to sinusoidal waves.
1. Correct — Vm = √2Vrms. 2. Correct — Vm = 1.414 × 220 ≈ 311 V. 3. Correct — The relation is valid for sinusoidal AC. 4. Incorrect — Peak voltage is always greater than RMS voltage. Therefore statements 1, 2 and 3 are correct.
- �� Option B → Includes incorrect statement 4.
- �� Option C → Includes incorrect statement 4.
- �� Option D → Includes incorrect statement 4.
Used
- Elimination
Application:
- Apply RMS–peak relationships.
Final Logic:
- Only statement 4 is incorrect.
Peak = 1.414 × RMS
9 The value of the integration of sin²(ωt) over one complete cycle divided by the period T, which is structurally used to derive the RMS current, is calculated precisely to:
�� RMS derivation uses sin². �� Average value of sin² over a cycle is 1/2. �� Basis of RMS formulas.
The RMS current derivation uses: (1/T) ∫ sin²(ωt) dt over one complete cycle. The average value of sin² over a full cycle is: 1/2 Therefore the required value is 1/2.
- �� Option A → Average of sin² is not zero.
- �� Option B → Average never reaches unity.
- �� Option D → This value appears after taking the square root in RMS derivation.
Used
- Direct Formula Recall
Application:
- Recall the standard trigonometric average value.
Final Logic:
- Average value of sin² over a complete cycle is 1/2.
sin² Average = 1/2
10 If an alternating current has a peak value of 1.414 A, what is the equivalent DC current that would produce the identical average Joule heating in a given resistor?
�� Equivalent DC current equals RMS current. �� Irms = Im/√2. �� RMS current gives same heating effect.
Given: Im = 1.414 A RMS current: Irms = Im/√2 Irms = 1.414/1.414 Irms = 1.0 A The equivalent DC current producing the same average heating effect is therefore 1.0 A.
- �� Option B → Exceeds peak current.
- �� Option C → Incorrect RMS calculation.
- �� Option D → Peak current is not equivalent DC current.
Used
- Substitution
Application:
- Use the RMS current formula directly.
Final Logic:
- Irms = 1.414/√2 = 1.0 A.
Equivalent DC = RMS
11 Consider the statements regarding rotating vector (phasor) analysis. Choose the correct statements.
1. Phasors rotate counter-clockwise with an angular frequency ω
2. The length of the phasor is explicitly proportional to the rms or peak value of the alternating quantity
3. Phasors adeptly represent scalar physical quantities mathematically
4. Phasors strictly represent physical vectors navigating in 3D space
�� Phasors rotate with angular frequency ω. �� Phasor length represents amplitude. �� Phasors are mathematical representations.
1. Correct — A phasor is represented as a rotating vector moving counter-clockwise with angular velocity ω. 2. Correct — The phasor length is proportional to the peak or RMS value of the AC quantity. 3. Correct — Voltage and current are scalar quantities, but phasors provide a convenient mathematical representation. 4. Incorrect — Phasors are not physical vectors moving in three-dimensional space; they are mathematical tools. Hence statements 1, 2 and 3 are correct.
- �� Option B → Includes incorrect statement 4.
- �� Option C → Includes incorrect statement 4.
- �� Option D → Includes incorrect statement 4.
Used
- Elimination
Application:
- Remove the statement that incorrectly interprets phasors as physical vectors.
Final Logic:
- Only statement 4 is incorrect.
Phasor = Mathematical Rotator
12 Choose the correct statements about the projection of phasors:
1. The vertical projection of the voltage phasor distinctly represents vm sin(ωt)
2. The projection gives the tangible value of the voltage at that specific instant
3. As the phasor physically rotates, the projection effectively generates a sinusoidal curve
4. The vertical component remains strictly constant over progressing time
�� Vertical projection gives instantaneous value. �� Projection varies sinusoidally. �� Projection is not constant.
1. Correct — The vertical projection of a rotating voltage phasor equals vm sin(ωt). 2. Correct — This projection represents the instantaneous value of voltage. 3. Correct — Continuous rotation produces a sinusoidal variation with time. 4. Incorrect — The vertical projection changes continuously and is not constant. Therefore statements 1, 2 and 3 are correct.
- �� Option B → Includes incorrect statement 4.
- �� Option C → Includes incorrect statement 4.
- �� Option D → Includes incorrect statement 4.
Used
- Elimination
Application:
- Identify the statement that contradicts sinusoidal variation.
Final Logic:
- The vertical projection changes with time and cannot remain constant.
Projection = Instantaneous Value
13 Choose the incorrect statement about angular frequency and frequency:
�� XL = ωL = 2πfL. �� Inductive reactance increases with frequency. �� Capacitive reactance decreases with frequency.
Inductive reactance is given by: XL = ωL = 2πfL Hence XL is directly proportional to frequency, not inversely proportional. Therefore statement C is incorrect. Statements A and B correctly describe angular frequency and phasor motion. Statement D is correct because: XC = 1/(ωC) which is inversely proportional to frequency.
- �� Option A → Correct definition of angular frequency.
- �� Option B → Correct description of phasor rotation.
- �� Option D → Correct relation for capacitive reactance.
Used
- Direct Formula Recall
Application:
- Use reactance formulas directly.
Final Logic:
- XL ∝ f, not 1/f.
Inductor Likes Frequency
14 Regarding the specific phase angle between voltage and current in basic AC circuits:
1. In a pure resistor, the phase angle is exactly zero
2. In a pure inductor, the current consistently lags the voltage by π/2
3. In a pure capacitor, the current predictably leads the voltage by π/2
4. The phase angle primarily dictates the amount of wattless current
Choose correct:
�� Resistor → phase difference zero. �� Inductor → current lags by π/2. �� Capacitor → current leads by π/2.
1. Correct — Voltage and current are in phase in a resistor. 2. Correct — In a pure inductor, current lags voltage by π/2. 3. Correct — In a pure capacitor, current leads voltage by π/2. 4. Though phase angle influences reactive behavior, the option set provided identifies only statements 1, 2 and 3 as the standard NCERT relationships. Hence Option C is the correct answer.
- �� Option A → Omits statement 3.
- �� Option B → Omits statement 1.
- �� Option D → Excludes two correct statements.
Used
- Direct Concept Recall
Application:
- Recall standard phase relationships in R, L and C circuits.
Final Logic:
- Statements 1, 2 and 3 are the fundamental phase-angle relations.
R = 0, L = Lag, C = Lead
15 Which of the following was explicitly NOT mentioned as a defining invention or conception of Nikola Tesla?
�� Tesla pioneered AC technology. �� Developed induction motor. �� Conceived rotating magnetic field.
Tesla is associated with the rotating magnetic field, induction motor and polyphase AC power systems. The modern electric battery was not one of Tesla's defining inventions. Therefore Option D is correct.
- �� Option A → A major Tesla contribution.
- �� Option B → Tesla invented the induction motor.
- �� Option C → Tesla pioneered polyphase AC systems.
Used
- Odd One Out
Application:
- Identify the invention unrelated to Tesla's AC innovations.
Final Logic:
- Battery technology is not a defining Tesla invention.
Tesla = AC, Not Battery
16 The primary electrical systems advocated enthusiastically by George Westinghouse and Thomas Edison respectively were:
�� Westinghouse supported AC. �� Edison supported DC. �� This conflict formed the "War of Currents."
George Westinghouse strongly promoted alternating current systems because of their advantages in transmission and voltage conversion. Thomas Edison advocated direct current systems. Hence the correct pairing is: Alternating current, Direct current.
- �� Option B → Reverses their positions.
- �� Option C → Not electrical systems.
- �� Option D → Incorrect association.
Used
- Historical Recall
Application:
- Recall the War of Currents.
Final Logic:
- Westinghouse → AC, Edison → DC.
West = AC, Edison = DC
17 Match List I with List II regarding transformers and power transmission:
| List I | List II |
|---|---|
| 1. Step-up transformer | a. Output coil |
| 2. Step-down transformer | b. Reduces voltage |
| 3. Primary coil | c. Increases voltage |
| 4. Secondary coil | d. Input coil |
�� Step-up increases voltage. �� Step-down reduces voltage. �� Primary is input coil. �� Secondary is output coil.
1 → c because a step-up transformer increases voltage. 2 → b because a step-down transformer decreases voltage. 3 → d because the primary coil receives input power. 4 → a because the secondary coil delivers output power. Therefore: 1-c, 2-b, 3-d, 4-a
- �� Option B → Step-up and step-down functions reversed.
- �� Option C → Primary and secondary coils interchanged.
- �� Option D → Multiple incorrect matches.
Used
- Option Grouping
Application:
- Match transformer components with functions.
Final Logic:
- Only Option A provides all correct pairings.
Primary = Input, Secondary = Output
18 In an AC distribution network, when electrical energy is transmitted economically over long distances,
�� Power loss = I²R. �� High voltage means low current. �� Lower current reduces losses.
For a given power: P = VI Increasing voltage reduces current. Since transmission losses are: Ploss = I²R reducing current greatly decreases power loss. Therefore high-voltage transmission is economically preferred.
- �� Option B → Voltage is stepped up, not down, during transmission.
- �� Option C → AC transmission is widely used.
- �� Option D → Low voltage increases current and losses.
Used
- Direct Formula Recall
Application:
- Use P = VI and I²R loss equations.
Final Logic:
- High voltage minimizes current and transmission loss.
High V → Low I → Low Loss
19 Choose the correct statements about AC voltage applied to a pure resistor:
1. The voltage and current are exactly in phase with each other
2. The minima, zero, and maxima of voltage and current naturally occur at the same respective times
3. Ohm's law fundamentally works equally well for AC and DC voltages in resistors
4. The average power dissipated predictably averages to zero
�� Voltage and current are in phase. �� Ohm's law applies. �� Average power is not zero.
1. Correct — Voltage and current remain in phase. 2. Correct — Both reach maxima, minima and zero simultaneously. 3. Correct — Ohm's law applies to a pure resistor for both AC and DC. 4. Incorrect — Average power is positive and equals I²R. Therefore statements 1, 2 and 3 are correct.
- �� Option B → Includes incorrect statement 4.
- �� Option C → Includes incorrect statement 4.
- �� Option D → Includes incorrect statement 4.
Used
- Elimination
Application:
- Use the power relation in a resistor.
Final Logic:
- Average power is not zero; statement 4 is false.
Resistor = In Phase + Positive Power
20 Identify the incorrect statement about the measurable current passing through a pure resistor in an AC circuit:
�� Current and voltage are in phase. �� im = vm/R. �� Power depends on i²R.
In a pure resistor: i = im sin(ωt) and v = vm sin(ωt) Both quantities are in phase, meaning the phase difference is zero. Therefore statement C is incorrect.
- �� Option A → Correct property of AC current.
- �� Option B → Correct expression from Ohm's law.
- �� Option D → Instantaneous power equals i²R.
Used
- Odd One Out
Application:
- Identify the statement inconsistent with resistive AC circuits.
Final Logic:
- A pure resistor has zero phase difference, not π/2.
Pure Resistor = Zero Phase Angle
