# AC Fundamentals, Circuit & Circuit Theory Objective Questions With Explanation Part-1

1. A sine wave has a frequency of 50 Hz. Its angular frequency is ...... radian/ second.
A. 100 Ï€
B. 50 Ï€
C. 25 Ï€
D. 5 Ï€

Explanation:
The angular frequency, Ï‰ = 2Ï€f = 2Ï€50 = 100 Ï€

2. The reactance offered by a capacitor to alternating current of frequency 50 Hz is 20 ohm. If frequency is increased to 100 Hz, reactance becomes ohms.
A. 2.5
B. 5
C. 10
D. 15

Explanation:
The capacitive reactance is given by,
Xc = 1 / (Ï‰ C)

Where Ï‰ = 2Ï€f
Xc = 1 / (2Ï€fC)

Capacitive reactance is inversely proportional to frequency
Xc1/Xc2 = f2/f1

Xc2 =Xc1 x f1/f2 = 20 x 50/100 =1000/100 = 10

3. The period of a wave is
A. the same as frequency
B. time required to complete one cycle
C. expressed in amperes
D. none of the above

Answer: B. time required to complete one cycle

Explanation:
• Wave Period (T) : The time taken by a particle of the medium to complete one vibration or Wave period is the time during which one complete wave is set up in a medium.
• The period of a wave is the time for a particle on a medium to make one complete vibrational cycle. Period, being a time, is measured in units of time such as seconds, hours, days or years.
• The period of orbit for the Earth around the Sun is approximately 365 days; it takes 365 days for the Earth to complete a cycle.
4. The form factor is the ratio of
A. peak value to r.m.s. value
B. r.m.s. value to average value
C. average value to r.m.s. value
D. none of the above

Answer: B. r.m.s. value to average value

Explanation:
• The Form factor is defined as the ratio of the RMS value to the average value of an alternating quantity.
• Crest Factor ‘or’ Peak Factor is defined as the ratio of the maximum value to the R.M.S value of an alternating quantity.
5. The period of a sine wave is 1/50 Its frequency is
A. 20 Hz
B. 30 Hz
C. 40 Hz
D. 50 Hz

Explanation:
The frequency is given by F = 1/T
Where T = Time Period

So  Time Period T =  1/F  = 1/50

So frequency is 50 Hz.

6. A heater is rated as 230 V,10 kW, AC. The value 230 V refers to
A. average voltage
B. r.m.s. voltage
C. peak voltage
D. none of the above

Explanation:
• The maximum value of the voltage is called peak voltage.
• When the peak voltage is divided by the square root of two, we get the r.m.s. voltage.
• The value of the AC voltage changes continuously with time. So, it is important to calculate the r.m.s. voltage. RMS voltage allows us to compare with the value of DC voltage which is constant. The rating of an electrical appliance is done in the form of an r.m.s. voltage value.
• So, the value 230 V refers to r.m.s. voltage.
7. If two sinusoids of the same frequency but of different amplitudes and phase angles are subtracted, the resultant is
A. a sinusoid of the same frequency
B. a sinusoid of half the original frequency
C. a sinusoid of double the frequency
D. not a sinusoid

Answer:  A. a sinusoid of the same frequency

Explanation:
• If two sinusoids of the same frequency but of different amplitudes and phase angles are subtracted, the resultant is a sinusoid of the same frequency

Important Notes:
• Voltmeter: The device that is used to measure the electrical potential difference between two points in an electric circuit is called a voltmeter.
• The voltmeter is connected in parallel with the circuit to measure the same voltage drop occurs across it.
• To measure DC voltage, a DC voltmeter is used.
• To measure AC voltage, an AC voltmeter or hot wire voltmeter is used.
• DC voltmeter can not measure AC voltages.
• When used in AC circuits, DC Voltmeter gives zero reading because the average value of alternating voltage over a full cycle is zero.
• So, the reading of the voltmeter will be 0 volts, as a DC voltmeter cannot be used for measuring AC potential difference as it is current direction oriented.
• To measure AC, the heating effect of the current is used because the heating effect does not depend on the direction of the flow of current.
• The hot wire Voltmeter or AC voltmeter works in the principle of heating effect.
• It measures the RMS value of voltage in AC.

8. The peak value of a sine wave is 200 V. Its average value is
A. 127.4 V
B. 141.4 V
C. 282.8 V
D. 200 V

Explanation:
The average value of sine wave is given by
Vavg = 2Vp/Ï€

Where Vp = Peak Voltage = 200V

Vavg = 2 x 200/Ï€ = 400/Ï€ = 400/3.14159 =127.4 V

9. The r.m.s. value of a sine wave is 100 A. Its peak value is
A. 70.7 A
B. 141.4 A
C. 150 A
D. 282.8 A

Explanation:
For sinusoidal alternating current the peak factor or amplitude factor can be expressed the ratio of maximum or peak value and rms value of alternating current.

So the peak value = rms value of alternating current × peak factor of alternating current

peak value = rms value of alternating current × 1.414

= 100 × 1.414 = 141.4 A.

Its peak value is 141.4 A.

10. Two waves of the same frequency have opposite phase when the phase angle between them is
A. 360°
B. 180°
C. 90°
D. 0°