1.) Define time constant for a R-L series circuit.

The time constant (τ) for an R-L series circuit is the time required for the current to reach 63.2% of its maximum
𝑳
value during growth or to decay to 36.8% of its initial value during decay. It is given by 𝝉 = 𝑹 , where L is inductance
and R is resistance.

2. What is the effect of frequency on capacitive reactance?

𝟏
Capacitive reactance (XC) decreases as the frequency (f) increases, according to 𝑿𝑪 = 𝟐𝝅𝒇𝑪 , where C is the
capacitance.

3. Which material is used in the core of a transformer?

Silicon steel is commonly used in transformer cores due to its high magnetic permeability and low hysteresis loss.

4. What is the condition for maximum starting torque of an induction motor?

The maximum starting torque occurs when the rotor resistance equals the rotor reactance (Rr = Xr)

5. What is the need for controlling the output voltage of an inverter?

Controlling the output voltage of an inverter is essential to regulate power flow, maintain voltage levels for specific
applications, and improve efficiency.

6. What is a fuse link?

A fuse link is the replaceable element within a fuse that melts when excessive current flows, thereby interrupting
the circuit to prevent damage.

7. Convert 4A source with its parallel resistance of 15Ω into its equivalent voltage source.
Using
𝑉 = 𝐼. 𝑅
𝑉 = 4 × 15 = 60𝑉.
Equivalent voltage source: 60V in series with a 15Ω resistance.

8. In series circuit analysis, why is current taken as the reference phasor?

In a series circuit, the same current flows through all components, making it the most logical and consistent
reference phasor for phase angle calculations.

9. In a transformer, maximum voltage regulation occurs at ______.

Maximum voltage regulation occurs at lagging power factor load.
10. What is meant by rotor frequency in a 3-phase induction motor?
Rotor frequency is the frequency of the induced current in the rotor and is given by fr = s⋅f, where s is slip and f is
the stator supply frequency.

11. When is steady-state ripple maximum for a chopper?

Steady-state ripple is maximum when the duty cycle (D) is either very small or very large.

12. What is the current that is considered safe for the human body?
About 9-10 mA is considered safe for the human body under normal conditions.

13. What is fuse?

A fuse is a protective device that interrupts the flow of excessive current by melting its internal link, safeguarding
electrical circuits from damage.

14. What is the efficiency of power transfer when maximum transfer of power occurs?
The efficiency of power transfer during maximum power transfer is 50%.

15. In a series R-L-C circuit, what is the condition for resonance?

Resonance occurs when the inductive reactance equals the capacitive reactance (XL = XC) or when the impedance
of the circuit is purely resistive.

16. What is a core type transformer?

A core type transformer is one in which the windings surround a considerable part of the core, and the core is a
rectangular frame with two limbs.

17. What is the basic principle of operation of alternators/DC generators?

They operate on Faraday's law of electromagnetic induction, which states that an electromotive force is induced in
a conductor when it cuts magnetic flux.

18. What is meant by duty cycle?

The duty cycle is the ratio of the ON time to the total time period of a waveform, usually expressed as a percentage.

19. What is the function of a transformer?

A transformer transfers electrical energy between circuits by stepping up or stepping down voltage levels while
maintaining the same frequency.
20. Define synchronous speed.
𝟏𝟐𝟎𝒇
Synchronous speed is the speed at which the magnetic field in a motor rotates, given by 𝑵𝑺 = , where f is the
𝑷
supply frequency and P is the number of poles.

21. What are the main classifications of an inverter?

Inverters are classified as:
1. Voltage Source Inverter (VSI).
2. Current Source Inverter (CSI).

22. What is a secondary cell?

A secondary cell is a rechargeable battery that can be charged, discharged, and reused multiple times, such as a
lithium-ion battery.

23. What will be the impedance of a coil containing resistance of 8.0Ω and an inductive reactance of 6.0Ω?
Impedance (Z) is given by:

𝒁 = √𝑹𝟐 + 𝑿𝟐𝑳 = √82 + 62 = √100 = 10Ω.

24. The full-load copper loss of a transformer is 1600 W. At half-load, what will be the copper loss?
Copper loss varies with the square of the load. At half-load:
Copper loss = 0.52 × 1600 = 0.25 × 1600 = 400𝑊.

𝑹
25. The bandwidth of a series R-L-C circuit at resonance is given by – 𝟐𝝅𝑳 .

26. Transformer core is laminated to reduce – Eddy current loss.

27. Power factor of AC resistive circuit is – unity.

28. For R-L-C series resonance circuit, line current at resonance frequency is – maximum.

29. Two impedances (10+j10) Ω and (10-j10) Ω are connected in parallel. Their equivalent impedance is –
𝟏 𝟏 𝟏
= +
𝒁𝒆𝒒𝒗 𝒁𝟏 𝒁𝟐
𝟏 𝟏 𝟏
= +
𝒁𝒆𝒒𝒗 𝟏𝟎 + 𝒋𝟏𝟎 𝟏𝟎 − 𝒋𝟏𝟎
𝟏𝟎 − 𝒋𝟏𝟎 𝟏𝟎 + 𝒋𝟏𝟎
= +
(𝟏𝟎 + 𝒋𝟏𝟎)(𝟏𝟎 − 𝒋𝟏𝟎) (𝟏𝟎 − 𝒋𝟏𝟎)(𝟏𝟎 + 𝒋𝟏𝟎)
𝟏𝟎 − 𝒋𝟏𝟎 𝟏𝟎 + 𝒋𝟏𝟎
= 𝟐 𝟐
+
(𝟏𝟎) − (𝒋𝟏𝟎) (𝟏𝟎)𝟐 − (𝒋𝟏𝟎)𝟐
 𝟏𝟎 − 𝒋𝟏𝟎 𝟏𝟎 + 𝒋𝟏𝟎
= + 𝒘𝒉𝒆𝒓𝒆, 𝒇𝒓𝒐𝒎 𝒑𝒓𝒆𝒗. 𝒔𝒕𝒆𝒑 𝒅𝒆𝒏𝒐𝒎𝒊𝒏𝒂𝒕𝒐𝒓 = 𝟏𝟎𝟎 − (−𝟏𝟎𝟎) = 𝟐𝟎𝟎
𝟐𝟎𝟎 𝟐𝟎𝟎
𝟏𝟎 𝟏𝟎 𝟏𝟎 𝟏𝟎
=( −𝒋 )+( +𝒋 )
𝟐𝟎𝟎 𝟐𝟎𝟎 𝟐𝟎𝟎 𝟐𝟎𝟎
(𝟎. 𝟎𝟓 − 𝒋𝟎. 𝟎𝟓) + (𝟎. 𝟎𝟓 + 𝒋𝟎. 𝟎𝟓) = 𝟎. 𝟎𝟓 + 𝟎. 𝟎𝟓 = 𝟎. 𝟏
𝟏
𝒁𝒆𝒒𝒗 = 𝟎.𝟏 = 𝟏𝟎𝛀.

30. The direction of rotation of a DC motor is given by – Fleming’s left-hand rule.

31. Why Rotor never runs at synchronous speed?

If the speed of the rotor is equal to the synchronous speed, no relative motion occurs between the rotating
magnetic field of the stator and the conductors of the rotor. Thus, the EMF is not induced on the conductor, and zero
current develops on it. Without current, the torque is also not produced.
Because of the above-mentioned reasons the rotor never rotates at the synchronous speed. The speed of the rotor
is always less than the speed of the rotating magnetic field.

32. What is Slip in induction motor?

Slip in Induction Motor is the relative speed between the rotating magnetic flux and rotor expressed in terms of per
unit synchronous speed. It is a dimensionless quantity. The value of slip in induction motor is can never be zero.
If Ns and Nr being the synchronous speed of rotating magnetic flux and rotor speed respectively, then the relative
speed between them is equal to (𝑁𝑠 − 𝑁𝑟 ). Therefore, slip is defined as
𝑵 𝑺 − 𝑵𝑹
𝑺𝒍𝒊𝒑 (𝑺) =
𝑵𝑺
• NS - synchronous speed (rpm)
• Nr – rotor speed (rpm)
As we know that, the speed of rotor cannot be equal to synchronous speed i.e., 𝑁𝑠 > 𝑁𝑟, the value of slip s is always
less than one. For induction motor, 0 < S < 1.

𝑵𝑷
𝑹𝒐𝒕𝒐𝒓 𝒇𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 (𝒇′ ) =
𝟏𝟐𝟎
Where,
• N – relative speed between magnetic field & the winding.
• P – no. of poles.
(𝑵𝑺 − 𝑵𝑹 ). 𝑷
→ 𝒇′ =
𝟏𝟐𝟎
𝒔. 𝑵𝑺 . 𝑷 𝟏𝟐𝟎𝒇
= = 𝒔. 𝒇 [∵ 𝑵𝑺 = ]
𝟏𝟐𝟎 𝑷
Where,
• S – Slip.
• f – supply frequency.
 𝑇𝑜𝑟𝑞𝑢𝑒 𝑜𝑓 𝑡ℎ𝑟𝑒𝑒 𝑝ℎ𝑎𝑠𝑒 𝑖𝑛𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑚𝑜𝑡𝑜𝑟, 𝑇 = 𝑘𝜙𝐼2 𝑐𝑜𝑠𝜙2
Where,
ϕ – flux per stator pole.
I2 - rotor current at standstill.
ϕ2 – angle between rotor emf & current.
k – a constant.
Now, let E2 = rotor emf at standstill. E2 ∝ ϕ.
∴ 𝑻 = 𝒌𝟏 𝑬𝟐 𝑰𝟐 𝒄𝒐𝒔𝝓𝟐
Where,
k1 - another constant.
Now,
𝑺𝒕𝒂𝒓𝒕𝒊𝒏𝒈 𝒕𝒐𝒓𝒒𝒖𝒆 𝑜𝑓 𝑎 3 − 𝑝ℎ𝑎𝑠𝑒 𝑖𝑛𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑚𝑜𝑡𝑜𝑟,

𝟑 𝑬𝟐𝟐 𝑹𝟐 𝟑
𝑻𝒔𝒕 = . [∵ 𝒌𝟏 = ]
𝟐𝝅𝑵𝑺 𝑹𝟐𝟐 + 𝑿𝟐𝟐 𝟐𝝅𝑵𝑺

Where,
R2 – rotor resistance per phase,
X2 – standstill rotor reactance.
Condition for maximum starting torque –

𝑹𝟐𝟐 + 𝑿𝟐𝟐 = 𝟐𝑹𝟐𝟐 [∵ 𝑹𝟐 = 𝑿𝟐 ]

And,

Torque under running conditions –

𝟑 𝒔𝑬𝟐𝟐 𝑹𝟐
𝑻= . 𝟐
𝟐𝝅𝑵𝑺 𝑹𝟐 + (𝒔𝑿𝟐 )𝟐

Starting torque is same at standstill & under running condition as s=1 at standstill.
maximum torque condition –
𝑹𝟐
𝒔=
𝑿𝟐

Rotor efficiency of 3-phase induction motor –

𝑷𝒎
𝜼𝒓 =
𝑷𝟐

Where,

Pm – rotor output/gross mechanical power developed,

P2 - rotor input
Efficiency of 3-phase induction motor –

𝑃𝑜𝑢𝑡
𝜂= × 100%
𝑃𝑖𝑛

Where,

Pin – electrical input to the motor,

Pout – power developed at shaft.