JEE Main - Power in AC circuits and basic transformers Online Test (MCQ Quiz)

1. In an AC circuit, the instantaneous power is given by the product of instantaneous voltage and instantaneous current. What is the term for the average value of this instantaneous power over a complete cycle?

A) Apparent Power B) Reactive Power C) True Power (or Real Power) D) Peak Power

2. The unit of apparent power in an AC circuit is:

A) Watt (W) B) Volt-Ampere (VA) C) VAR (Volt-Ampere Reactive) D) Joule (J)

3. In a purely resistive AC circuit, the voltage and current are in phase. In this case, what is the power factor?

A) 0 B) 0.5 C) 1 D) Infinity

4. What is the formula for true power (P) in an AC circuit, where Vrms is the RMS voltage, Irms is the RMS current, and cos(phi) is the power factor?

A) P = Vrms * Irms B) P = Vrms * Irms * sin(phi) C) P = Vrms * Irms * cos(phi) D) P = Irms^2 * R

5. Reactive power (Q) in an AC circuit is associated with:

A) Energy dissipated as heat B) Energy stored and returned by reactive components (inductors and capacitors) C) The product of RMS voltage and RMS current D) The maximum power delivered in a cycle

6. The relationship between apparent power (S), true power (P), and reactive power (Q) in an AC circuit is given by:

A) S = P + Q B) S^2 = P^2 - Q^2 C) S = P * Q D) S^2 = P^2 + Q^2

7. A transformer is a device that transfers electrical energy from one AC circuit to another through electromagnetic induction. What is the primary principle behind its operation?

A) Ohm's Law B) Joule's Law C) Faraday's Law of Electromagnetic Induction D) Ampere's Law

8. In an ideal transformer, the ratio of the number of turns in the secondary coil (Ns) to the number of turns in the primary coil (Np) is equal to the ratio of:

A) Primary voltage to secondary voltage B) Secondary current to primary current C) Secondary voltage to primary voltage D) Primary current to secondary current

9. For an ideal transformer, if the number of turns in the secondary coil is greater than the number of turns in the primary coil (Ns > Np), it is a(n):

A) Step-down transformer B) Step-up transformer C) Isolation transformer D) Autotransformer

10. In an ideal step-down transformer, the voltage is decreased. What happens to the current?

A) It decreases proportionally B) It increases proportionally C) It remains the same D) It becomes zero

11. The voltage transformation ratio (or turns ratio) of a transformer is defined as k = Ns / Np. If k = 0.5, the transformer is a:

A) Step-up transformer B) Step-down transformer C) Isolation transformer D) Constant voltage transformer

12. In an ideal transformer, the power in the primary coil is equal to the power in the secondary coil. This implies that:

A) Vp * Ip = Vs * Is B) Vp / Ip = Vs / Is C) Vp * Is = Vs * Ip D) Vp + Ip = Vs + Is

13. A transformer is used to step down the voltage from 220 V to 110 V. If the primary coil has 1000 turns, how many turns does the secondary coil have?

A) 2000 turns B) 500 turns C) 100 turns D) 10 turns

14. If the secondary current in an ideal transformer is 2 A and the primary current is 0.5 A, what is the ratio of turns Ns/Np?

A) 0.25 B) 4 C) 0.5 D) 2

15. The core of a transformer is usually made of laminated soft iron. Why is it laminated?

A) To increase magnetic flux B) To reduce hysteresis loss C) To reduce eddy currents D) To increase electrical resistance

16. Which type of loss in a transformer is primarily responsible for the heat generated in the windings due to the resistance of the wire?

A) Eddy current loss B) Hysteresis loss C) Copper loss (I^2R loss) D) Dielectric loss

17. Hysteresis loss in a transformer core occurs due to:

A) Rapid changes in magnetic flux B) The resistance of the core material C) The repeated magnetization and demagnetization of the core material D) The flow of induced currents in the core

18. What is the main purpose of using a soft iron core in a transformer?

A) To increase resistance B) To provide a path of low reluctance for magnetic flux C) To insulate the windings D) To reduce eddy currents

19. In a real transformer, the efficiency is always less than 100%. This is due to:

A) Perfect magnetic coupling B) No core losses C) Various types of energy losses (copper, iron, etc.) D) Ideal voltage and current transformation

20. The efficiency (η) of a transformer is defined as:

A) Output power / Input power B) Input power / Output power C) Output power / (Output power + Losses) D) (Output power + Losses) / Output power

21. For maximum efficiency in a transformer, the copper losses should be equal to:

A) Hysteresis losses B) Eddy current losses C) Iron losses (or core losses) D) Stray losses

22. An AC voltage source of 200 V is connected to the primary coil of a transformer. The secondary coil has 100 turns, and the primary coil has 500 turns. What is the secondary voltage?

A) 1000 V B) 400 V C) 40 V D) 20 V

23. If a transformer has Np = 200 turns and Ns = 1000 turns, and the primary voltage is 12 V, what is the secondary voltage?

A) 2.4 V B) 60 V C) 120 V D) 240 V

24. In a city's power distribution system, voltage is stepped up to very high values for transmission over long distances. What type of transformer is used for this purpose?

A) Step-down transformer B) Step-up transformer C) Isolation transformer D) Rectifier transformer

25. At the receiving end of the power grid, the high transmission voltage is reduced to a safer level for household use. What type of transformer is used here?

A) Step-up transformer B) Step-down transformer C) Autotransformer D) Welding transformer

26. An AC circuit has a voltage of 230 V and a current of 5 A. If the power factor is 0.8, what is the true power consumed?

A) 1150 W B) 920 W C) 1840 W D) 2300 W

27. If the apparent power in an AC circuit is 1000 VA and the true power is 800 W, what is the reactive power?

A) 200 VAR B) 600 VAR C) 1000 VAR D) 1800 VAR

28. A transformer is rated at 10 kVA. This rating refers to the:

A) True power output B) Reactive power output C) Apparent power output D) Efficiency

29. In an AC circuit, if the voltage leads the current, the power factor is:

A) Leading B) Lagging C) Unity D) Zero

30. An inductive load in an AC circuit causes the current to:

A) Lead the voltage B) Lag the voltage C) Be in phase with the voltage D) Become zero

31. A transformer with Ns = Np is an:

A) Step-up transformer B) Step-down transformer C) Isolation transformer D) Autotransformer

32. What is the purpose of an isolation transformer?

A) To change voltage levels significantly B) To reduce power loss C) To provide electrical isolation between the primary and secondary circuits without changing the voltage D) To increase current

33. In a real transformer, the ratio of secondary voltage to primary voltage (Vs/Vp) is slightly different from the turns ratio (Ns/Np) due to:

A) Increased magnetic flux B) Leakage flux and winding resistance C) Higher power factor D) Reduced eddy currents

34. The term 'power factor' represents the ratio of:

A) Reactive power to apparent power B) True power to apparent power C) Apparent power to true power D) True power to reactive power

35. A transformer is used to convert high voltage AC to low voltage AC. This is essential for:

A) Increasing transmission efficiency B) Reducing power generation cost C) Making electricity safe for domestic use D) Reducing magnetic field interference

36. Consider an AC circuit with voltage V(t) = Vm sin(ωt) and current I(t) = Im sin(ωt - φ). The instantaneous power is P(t) = V(t)I(t). The average power over a cycle is:

A) (Vm * Im) / 2 B) (Vm * Im) / √2 C) (Vm * Im / 2) * cos(φ) D) Vm * Im * cos(φ)

37. Which of the following losses in a transformer is independent of the load?

A) Copper loss B) Iron loss C) Stray loss D) Total loss

38. If the input power to a transformer is 1000 W and the output power is 950 W, what is the power loss?

A) 50 W B) 950 W C) 1000 W D) 1950 W

39. An autotransformer differs from a conventional transformer in that it:

A) Has two separate windings B) Uses a non-magnetic core C) Has a single winding common to both primary and secondary circuits D) Operates on DC supply

40. What is the main advantage of an autotransformer over a two-winding transformer for certain applications?

A) Higher efficiency for large voltage changes B) Greater electrical isolation C) Reduced size and cost for small voltage changes D) Simpler construction

41. In a purely capacitive AC circuit, the current:

A) Leads the voltage by 90 degrees B) Lags the voltage by 90 degrees C) Is in phase with the voltage D) Is zero

42. The power dissipated in a purely inductive or purely capacitive AC circuit is:

A) Maximum B) Zero C) Equal to apparent power D) Equal to reactive power

43. Which component in an AC circuit is responsible for storing energy in an electric field?

A) Resistor B) Inductor C) Capacitor D) Transformer

44. Which component in an AC circuit is responsible for storing energy in a magnetic field?

A) Resistor B) Inductor C) Capacitor D) Transformer

45. The rating of a transformer is typically given in kVA. Why is it not given in kW?

A) Because transformers do not deliver real power B) Because the power factor of the load is not known at the time of manufacturing C) Because transformers are primarily reactive devices D) Because kW is a unit of energy, not power

46. If a transformer is overloaded, which type of loss is most likely to increase significantly and cause overheating?

A) Iron loss B) Hysteresis loss C) Copper loss D) Eddy current loss

47. The primary winding of a transformer is connected to an AC source. If the secondary is open-circuited, the current flowing in the primary is called:

A) Load current B) Magnetizing current C) Full-load current D) Short-circuit current

48. A transformer's ability to transfer power from primary to secondary is dependent on:

A) The frequency of the AC supply B) The voltage of the AC supply C) The magnetic coupling between the coils D) All of the above

49. In an AC circuit, the sum of true power and reactive power is equal to:

A) Apparent power B) Power factor C) Impedance D) Current squared

Power in AC circuits and basic transformers - Online Test

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