Wave form alternating quantity

The alternating quantity may be either voltage or current or flux. Accordingly, the wave form is known as voltage wave form, current wave form or flux wave form. There are many types of wave forms. Some examples are

(a) Sinusoidal wave form,

(b) Rectangular wave form,

(d) Saw-tooth wave form

(e) Trapezoidal wave form

(f) Stepped wave form and so on.

⚡ Waveform Types – MCQs (with Answers & Explanations)-

Q1. Which of the following waveforms represents a smooth periodic oscillation?

(a) Rectangular wave
(b) Saw-tooth wave
(c) Sinusoidal wave
(d) Stepped wave

✅ Answer: (c) Sinusoidal wave
Explanation:
A sinusoidal wave is the smoothest and naturally occurring waveform, found in AC supply, signals, and harmonics.

Q2. A waveform that switches instantly between two levels (high and low) is called:

(a) Triangular wave
(b) Rectangular wave
(c) Sinusoidal wave
(d) Trapezoidal wave

✅ Answer: (b) Rectangular wave
Explanation:
Rectangular waves have abrupt transitions between two fixed values, used in digital circuits and switching systems.

Q3. In which waveform does voltage increase and decrease linearly with time?

(a) Triangular wave
(b) Rectangular wave
(c) Saw-tooth wave
(d) Stepped wave

✅ Answer: (a) Triangular wave
Explanation:
Triangular waves rise and fall at a constant slope, forming a linear ramp up and ramp down.

Q4. Which waveform has a slow rise and an abrupt sudden fall?

(a) Sinusoidal wave
(b) Triangular wave
(c) Trapezoidal wave
(d) Saw-tooth wave

✅ Answer: (d) Saw-tooth wave
Explanation:
A saw-tooth wave has a gradual rise (or fall) followed by an instantaneous drop (or rise), like the teeth of a saw.

Q5. Which waveform has flat tops and flat bottoms with sloping rise/fall edges?

(a) Trapezoidal wave
(b) Triangular wave
(c) Sinusoidal wave
(d) Stepped wave

✅ Answer: (a) Trapezoidal wave
Explanation:
In trapezoidal waves, rise and fall are sloped, while the top portion is flat — similar to a trapezoid shape.

Q6. A waveform that increases in small discrete voltage levels instead of a smooth slope is called:

(a) Saw-tooth
(b) Rectangular
(c) Stepped waveform
(d) Sinusoidal

✅ Answer: (c) Stepped waveform
Explanation:
Stepped waveforms change gradually but in steps, commonly seen in multilevel inverters.

Q7. Which waveform contains the highest harmonic content?

(a) Sinusoidal
(b) Triangular
(c) Rectangular
(d) Stepped wave

✅ Answer: (c) Rectangular
Explanation:
Rectangular (square) waves have strong odd harmonics, giving high harmonic distortion.

Q8. Which waveform is MOST ideal for power transmission systems?

(a) Rectangular
(b) Sinusoidal
(c) Stepped
(d) Saw-tooth

✅ Answer: (b) Sinusoidal
Explanation:
Sinusoidal waves cause the least losses, zero harmonics (ideal), and best power factor properties.

Q9. A waveform commonly produced in switching power supplies (SMPS) is:

(a) Sinusoidal
(b) Trapezoidal
(c) Stepped
(d) Saw-tooth

✅ Answer: (d) Saw-tooth
Explanation:
SMPS circuits use saw-tooth signals for PWM modulation and ramp control.

Q10. A triangular wave differs from a saw-tooth because:

(a) It has sudden rise and slow fall
(b) Rise and fall both are linear
(c) It has abrupt transition at peak
(d) It has a flat top

✅ Answer: (b) Rise and fall both are linear
Explanation:
Unlike saw-tooth, triangular waves have symmetric linear slopes for both rising and falling edges.

Q11. Which waveform is used to generate PWM with uniform slope control?

(a) Trapezoidal
(b) Triangular
(c) Sinusoidal
(d) Stepped

✅ Answer: (b) Triangular
Explanation:
Triangular waves are used as carrier signals in PWM systems due to their linear rising/falling slopes.

Q12. In a stepped waveform, more steps lead to:

(a) More distortion
(b) Lower RMS value
(c) Waveform closer to sine wave
(d) Abrupt transitions

✅ Answer: (c) Waveform closer to sine wave
Explanation:
Increasing the number of steps makes the output smoother, like in multilevel inverters.

Q13. Which waveform is generated when an integrator circuit processes a square wave?

(a) Triangular wave
(b) Saw-tooth wave
(c) Sinusoidal wave
(d) Trapezoidal wave

✅ Answer: (a) Triangular wave
Explanation:
Integrators convert square waves into linear ramp (triangular) waves.

Q14. A trapezoidal waveform is mostly used in:

(a) Audio amplifiers
(b) Digital logic circuits
(c) Motor drive switching circuits
(d) RF communication

✅ Answer: (c) Motor drive switching circuits
Explanation:
Trapezoidal waves reduce motor noise and harmonics and are used in BLDC/AC drive control.

Q15. Saw-tooth waves are commonly used in:

(a) Oscilloscopes
(b) 3-phase inverters
(c) Transformers
(d) Power cables

✅ Answer: (a) Oscilloscopes
Explanation:
In oscilloscopes, the beam sweeps across the screen using a saw-tooth ramp wave.

ANALYSIS OF AC CIRCUIT-

It is assumed that the sinusoidally varying voltage is connected to

(a) purely resistive

(b) purely inductive and

In each case it is required to find the following quantities

1. The expression for the instantaneous current.

2. The polar form of voltage and current

3. The phasor diagram.

4. Ratio of voltage to current

5. Average power

6. Phase angle between voltage and current and hence power factor.

⚡ AC Circuit Analysis – MCQs (With Answers & Explanations)-

Q1. In a purely resistive AC circuit, the phase difference between voltage and current is:

(a) 90°
(b) -90°
(c) 0°
(d) 180°

✅ Answer: (c) 0°
Explanation:
In a resistor, voltage and current rise & fall together.
→ No phase shift → PF = 1.

Q2. In a purely inductive circuit, the current expression is:

Voltage: $v = V_m \sin(\omega t)$
The current will be:
(a) Peaks early
(b) Lags voltage by 90°
(c) Leads voltage by 90°
(d) Remains constant

✅ Answer: (b) Lags voltage by 90°
Explanation:
Inductor opposes change in current → current lags by 90°
$i = I_m \sin(\omega t - 90^\circ)$

Q3. In a purely capacitive AC circuit, current:

(a) Leads voltage by 90°
(b) Lags voltage by 90°
(c) Is in phase
(d) Opposite in phase

✅ Answer: (a) Leads voltage by 90°
Explanation:
Capacitor allows current to flow first (charging effect) → current leads.

Q4. In a resistive AC circuit, the ratio V/I gives:

(a) Reactance
(b) Impedance
(c) Resistance
(d) Admittance

✅ Answer: (c) Resistance
Explanation:
For pure R:
$V/I = R$

Q5. The polar form of voltage $v = V_m \sin(\omega t)$ is:

(a) $V_m ∠90°$
(b) $V_rms ∠0°$
(c) $V_rms ∠90°$
(d) $V_m ∠0°$

✅ Answer: (b) $V_{rms} ∠0°$
Explanation:
We always take voltage reference at 0° in AC analysis.

Q6. In a purely inductive circuit, the impedance is:

(a) R
(b) XC
(c) XL
(d) Z = R – jXL

✅ Answer: (c) XL
Explanation:
For pure L → $Z = j X_L$

Q7. The average power absorbed in a purely inductive or capacitive circuit is:

(a) Maximum
(b) Minimum
(c) Zero
(d) Half the real power

✅ Answer: (c) Zero
Explanation:
For pure L or C,
PF = cos(±90°) = 0 → $P_{avg} = 0$

Q8. The power factor of a purely resistive circuit is:

(a) 0
(b) 1
(c) 0.5
(d) Depends on R

✅ Answer: (b) 1
Explanation:
Voltage and current are in phase → PF = 1.

Q9. In a capacitor, the ratio V/I gives:

(a) Capacitive reactance
(b) Inductive reactance
(c) Resistance
(d) Impedance only for resistor

✅ Answer: (a) Capacitive reactance
Explanation:
For pure C →
$V/I = X_C = \frac{1}{\omega C}$

Q10. Which phasor diagram is correct for a purely RESISTIVE circuit?

(a) Voltage ahead of current
(b) Current ahead of voltage
(c) V and I on same line
(d) V & I perpendicular

✅ Answer: (c) V and I on same line
Explanation:
In resistive circuits → both are in phase.

Q11. In an inductive circuit, the phasor diagram shows:

(a) Current leading voltage
(b) Voltage leading current
(c) No phase difference
(d) Voltage & current opposite

✅ Answer: (b) Voltage leading current
Explanation:
Inductive rule: V leads I by 90°.

Q12. Instantaneous current for a purely resistive circuit:

Given $v = V_m \sin(\omega t)$ ,
(a) $i = I_m \sin(\omega t - 90°)$
(b) $i = I_m \sin(\omega t + 90°)$
(c) $i = I_m \sin(\omega t)$
(d) $i = 0$

✅ Answer: (c) $i = I_m \sin(\omega t)$
Explanation:
No phase difference in pure resistance.

Q13. The power factor of a purely inductive circuit is:

(a) +1
(b) –1
(c) 0
(d) 0.5

✅ Answer: (c) 0
Explanation:
Phase difference = 90° → PF = 0.

Q14. In a capacitive circuit, the phasor diagram shows:

(a) I leads V
(b) V leads I
(c) No shift
(d) 180° shift

✅ Answer: (a) I leads V
Explanation:
Capacitive rule: Current leads by 90°.

Q15. Which circuit absorbs maximum average power?

(a) Purely resistive
(b) Purely inductive
(c) Purely capacitive
(d) All equal

✅ Answer: (a) Purely resistive
Explanation:
Only R absorbs real power.
For L & C → Power = 0.

Q16. Impedance in polar form for a purely resistive circuit:

(a) $R ∠90°$
(b) $R ∠0°$
(c) $R ∠-90°$
(d) $R ∠180°$

✅ Answer: (b) $R ∠0°$
Explanation:
Resistance has no imaginary component → angle = 0°.

Q17. The instantaneous current for a capacitive circuit is:

(a) $i = I_m \sin(\omega t - 90°)$
(b) $i = I_m \sin(\omega t + 90°)$
(c) $i = I_m \cos(\omega t - 90°)$
(d) $i = 0$

✅ Answer: (b) $i = I_m \sin(\omega t + 90°)$
Explanation:
Current leads voltage by 90° in capacitor.

Q18. For a purely inductive load, the power waveform:

(a) Always positive
(b) Always negative
(c) Alternates positive and negative equally
(d) Zero

✅ Answer: (c) Alternates positive and negative equally
Explanation:
Power oscillates around zero → average power = 0.

Q19. Which circuit stores energy in a magnetic field?

(a) Pure R
(b) Pure L
(c) Pure C
(d) All

✅ Answer: (b) Pure L
Explanation:
Inductor stores energy in magnetic field.

Q20. Which circuit stores energy in an electric field?

(a) Pure R
(b) Pure L
(c) Pure C
(d) None

✅ Answer: (c) Pure C
Explanation:
Capacitor stores electrical energy in its electric field.