Questions & explanations
1. Which of the following correctly identifies a source of energy loss in a transformer and an appropriate method to reduce it?
- Hysteresis loss – reduced by using a laminated core
- Eddy current loss – reduced by using a core of high resistivity material
- Copper loss – reduced by using a core of high magnetic permeability
- Flux leakage – reduced by using a core with low hysteresis loss
Answer: Eddy current loss – reduced by using a core of high resistivity material
Eddy current loss is minimized by using a core material with high electrical resistivity (e.g., ferrites or laminated sheets) to reduce induced currents. Hysteresis loss is reduced by using soft magnetic materials with a narrow hysteresis loop, not lamination. Copper loss is reduced by using thick conductors, not core permeability. Flux leakage is reduced by using a closed magnetic circuit.
2. A sinusoidal voltage v = V₀ sin ωt is applied across a pure resistor R. The current through the resistor is:
- i = (V₀/R) sin ωt
- i = (V₀/R) sin (ωt + π/2)
- i = (V₀/R) sin (ωt – π/2)
- i = (V₀/R) cos ωt
Answer: i = (V₀/R) sin ωt
In a pure resistive circuit, voltage and current are in phase, so the current has the same sinusoidal form as the voltage without any phase shift. Option A correctly shows current proportional to sin ωt. Options B and C introduce phase shifts of ±90°, which occur in inductive or capacitive circuits, and option D uses cos ωt, which is equivalent to a 90° phase shift.
3. The average power consumed over one complete cycle in a purely inductive AC circuit is:
- Vʀᴍꜱ Iʀᴍꜱ
- Zero
- Vʀᴍꜱ Iʀᴍꜱ / 2
- Vʀᴍꜱ Iʀᴍꜱ / √2
Answer: Zero
In a purely inductive circuit, the voltage and current are 90° out of phase (current lags). The average power is P = Vʀᴍꜱ Iʀᴍꜱ cos φ, and cos 90° = 0, so the average power is zero. The same is true for a purely capacitive circuit. Option A gives the power for a resistive circuit, and options C and D are numerically incorrect for these components.
4. The root-mean-square (rms) value of an alternating current is defined as:
- The peak value divided by 2
- The average value over half a cycle
- The value of a steady direct current that produces the same heating effect in a resistor as the alternating current
- The instantaneous value at t = 0
Answer: The value of a steady direct current that produces the same heating effect in a resistor as the alternating current
The rms value of an alternating current is the equivalent steady direct current that would dissipate the same amount of power in a given resistor. Options A, B, and D are incorrect definitions; A gives half the peak, B gives the average (which is zero for a full cycle), and D is the instantaneous value at a specific time.
5. What is the fundamental principle behind the working of a transformer?
- Self-induction
- Mutual induction between two coils
- Electromagnetic induction due to a changing magnetic field
- Electrostatic induction
Answer: Mutual induction between two coils
A transformer works on the principle of mutual induction, where a changing current in the primary coil induces an emf in the secondary coil through a common magnetic core. Self-induction involves a single coil, electromagnetic induction is a broader phenomenon, and electrostatic induction is unrelated.
6. If the frequency of an AC source is doubled, which of the following correctly describes the change in reactance?
- Inductive reactance increases, capacitive reactance decreases
- Both inductive and capacitive reactance increase
- Both inductive and capacitive reactance decrease
- Inductive reactance decreases, capacitive reactance increases
Answer: Inductive reactance increases, capacitive reactance decreases
Inductive reactance Xₗ = 2πfL is directly proportional to frequency, so doubling f doubles Xₗ. Capacitive reactance X꜀ = 1/(2πfC) is inversely proportional to frequency, so doubling f halves X꜀. Hence option A is correct; the other options are opposite or incorrect.
7. For an alternating current (AC) circuit containing pure components, which of the following is correct?
- Voltage leads current by 90° in a pure capacitor
- Current leads voltage by 90° in a pure inductor
- Voltage and current are in phase in a pure resistor
- Current leads voltage by 90° in a pure resistor
Answer: Voltage and current are in phase in a pure resistor
In a pure resistor, voltage and current are exactly in phase (0° phase difference). In a pure inductor, current lags voltage by 90° (voltage leads). In a pure capacitor, current leads voltage by 90° (voltage lags). Therefore, only option C is correct.
8. For a sinusoidal alternating voltage of peak value 100 V, the rms value is:
- 100 V
- 50 V
- 70.7 V
- 100/√3 V
Answer: 70.7 V
For a sinusoidal waveform, the rms value equals the peak value divided by √2. Here, 100 V / √2 ≈ 70.7 V. The other options are incorrect: 100 V is the peak, 50 V is half the peak, and 100/√3 is approximately 57.7 V.
9. In an ideal transformer, if the secondary coil has twice the number of turns as the primary, what is the relationship between primary current (Ip) and secondary current (Is)?
- Is = 2 Ip
- Is = Ip/2
- Is = Ip
- Is = 4 Ip
Answer: Is = Ip/2
For an ideal transformer, power input equals power output: Vp Ip = Vs Is. Since Vs/Vp = Ns/Np = 2, we have Ip/Is = 2, so Is = Ip/2. The current ratio is inversely proportional to the turns ratio.
10. The average power consumed in an AC circuit is zero when the current is wattless. This occurs when the phase angle between voltage and current is:
- 0°
- 45°
- 90°
- 180°
Answer: 90°
When the phase angle is 90°, the power factor cos φ = 0, so the average power P = V_rms I_rms cos φ = 0. Such a current that does not contribute to power dissipation is called wattless current.
11. What is the primary reason for using step-up transformers at the generating station before transmitting power over long distances?
- To increase current for better transmission
- To increase voltage and decrease current, thereby reducing power loss
- To convert AC to DC
- To change the frequency to reduce losses
Answer: To increase voltage and decrease current, thereby reducing power loss
Step-up transformers increase voltage, which reduces current for the same power (P = VI). Lower current reduces I²R losses in the transmission lines, improving efficiency over long distances.
12. In a series LCR circuit connected to an AC source, the phasor diagram is drawn with the current as the reference phasor. Which of the following statements is correct?
- The voltage across the resistor leads the current by 90°.
- The voltage across the inductor lags the current by 90°.
- The voltage across the capacitor lags the current by 90°.
- The voltage across the inductor and the capacitor are in phase.
Answer: The voltage across the capacitor lags the current by 90°.
In a pure resistor, voltage and current are in phase. In a pure inductor, voltage leads current by 90°. In a pure capacitor, voltage lags current by 90°. Therefore, option C is correct.