Q. 1. Why sinusoidal wave shape is insisted for voltages and currents while generating, transmitting and utilizing ac electric power?
Ans. Sinusoidal wave shape is insisted for voltages and currents while generating, transmitting and utilizing ac electrical power because it has following advantages.
- Sinusoidal voltages and currents produce minimum disturbance in the electrical circuits during operation.
- Sinusoidal voltages and currents cause less (noise) to nearby communication circuits (telephone lines etc.).
- Sinusoidal voltages and currents result in low iron as well as low copper losses in transformers, and ac rotating machines for a given output. So, ac machines with sinusoidal voltages and currents operate at higher efficiency.
Q. 2. What do you understand by ω ?
Ans. Each cycle of a sinusoidal wave spans 2π radians. Hence, if this quantity is divided by the time period, angular velocity of the sinusoidal wave is obtained. It is denoted by ω and is expressed in radians per second.
Q.3. Why the rms value of an alternating current or voltage is used to denote its amplitude?
Ans. RMS value of an alternating current or voltage is used to denote its amplitude because it is related to the power developed in a resistance by the alternating current or voltage.
Q. 4. What is rms value of an alternating current?
Ans. The effective or rms value of an alternating current is given by that steady current which when flows through a given resistance for a given time produces the same amount of heat as when the alternating current is flowing through the same resistance for the same time duration.
Q.5. Do wave shapes other than sine wave have effective value?
Ans. Yes, all the wave shapes including the sine wave have effective value since in each half cycle of the wave, work is being done. Actually, the effective value of an alternating wave (sinusoidal or non-sinusoidal) is defined as below:
The rms or effective value of an alternating current or voltage is given by that steady current or voltage which when flows or applied to a given resistance for a given time produces the same amount of heat as when the alternating current or voltage is following or applied to the same resistance for the same time.
Q. 6. Differentiate between form factor and peak factor.
Ans. Form factor is defined as the ratio of the effective value to the average or mean value of the periodic wave while peak factor is defined as the ratio of peak or maximum value to the effective or rms value of the periodic wave.
Q. 7. What is significance of form factor?
Ans. Form factor s a mean of relating the mean value with the effective or rms value of alternating quantity and it is useful in determination of effective or rms values of the alternating quantities whose mean or average values over half a period can be determined conveniently.
Q. 8. What is the significance of peak factor?
Ans. Knowledge of peak factor of an alternating voltage is very essential in connection with determining the dielectric strength since the dielectric stress developed in an insulting material is proportional to the peak value of the voltage applied to it.
Q. 9. What is the significance of the phasor representation of an alternating quantity?
Ans. The phase representation of an alternating quantity enables us to understand its magnitude and position with respect to reference line.
Q. 10. What do you mean by phase and phase difference?
Ans. The phase of an alternating quantity (voltage or current) at any instant is defined as the fractional part of a cycle through which the quantity has advanced while the phase difference may be defined as the angular displacement between the maximum positive values of the two phasors representation the two quantities having the same frequency.
Q. 11. 220 volt a.c. is more dangerous than 220 volt d.c. Why?
Ans. 220 volt a.c. means the effective or virtual value of a.c. is 220 volt, i.e. Ev = 220 volt.
As peak value
But 220 volt d.c. has the same peak value (i.e. 220 volt only)
Moreover, the shock of a.c. is attractive and that of d.c. is repulsive.
Hence 220 volt a.c. is more denger than 220 volt d.c.
Q. 12. Can we use 15 c/s. a.c. for lighting purpose?
Ans. Yes, we van use 15 c/s. a.c. for lighting purpose. The fluctuation in current will be so rapid (30 times/second) that the bulb will appear glowing continuously due to persistence of vision.
Q. 13. The resistance of a coil for direct current is 10 ohm. An alternating current is sent through it. Will its resistance remain the same?
Ans. No, the resistance of the coil will not remain the same. It will increase to
Q. 14. An electric heater is heated turn by turn with d.c. and a.c. keeping pot. Diff. across the ends of the heater same. Will the rate of production of heat in the two cases be same? Explain.
Ans. An electric heater is in the form of a coil of ohmic resistance R and inductance L. on d.c. supply, resistance = R. On a.c. supply, impedance = which is obviously more.
When potential difference is constant, heat produced/sec is inversely proportional to resistance. Hence heat produced/sec in case of a.c. will be less.
Summery | Highlight of Alternating Current
- An alternating quantity (voltage or current) is one which changes continuously in magnitude and alternates in direction at regular intervals of time.
An alternating quantity that varies sinusoidal (i.e. according to the sin of angle θ) is called the sinusoidal quantity.
Sinusoidal quantities are expressed as
- The shape of the curve of the voltage or current when plotted against time as abscissa (base) is called the waveform.
- When a periodic wave, such as sinusoidal wave, goes through one complete set of positive and negative values it is said to have completed one cycle. One cycle corresponds to 3600 or 2 π
Alternation is one half of cycle and corresponds to 1800 or π radians.
- The time taken in seconds by an alternating quantity to complete one cycle is known as time period or periodic time (T), while the number of cycles completed per second by an alternating quantity is known as frequency (f).
- Angular velocity, radians per second.
- In a multipolar machine, the number of cycles completed per second by generated emf.
f = Pairs of poles × number of revolutions made per second
- The maximum value, positive or negative, which an alternating quantity attains during one cycle is called the amplitude of the alternating quantity.
- The general expression for an alternating voltage and current are given as
Where is the phase angle in degree or radians.
The coefficient of the sine of the time angle gives maximum or peak value of the alternating quantity (emf, voltage or current).
Coefficient of time t divided by 2 π. It gives the frequency of the periodic wave.
- The average (or mean) value of an alternating current is expressed by that steady current (dc) which transfer across any circuit the same change as transferred by the alternating current.
Average or mean value of alternating current is given as
For sinusoidal current
- Effective or virtual value of alternating current or voltage is equal to the square root of the mean of the squares of successive ordinates and that is why it is known as roof-mean square (rms) value.
The rms or effective value of an alternating current or voltage is given by that steady current or voltage which when flows or applied to a given resistance for a given time produces the same amount of heat as when the alternating current or voltage following or applied to the same resistance for the same time.
For sinusoidal current,
- The ratio of rms value to the average value of a waveform is known as form factor. For sinusoidal wave its value is 1.11.
- The ratio of maximum value to the rms value of a waveform is known as peak factor. For sinusoidal wave its value is or 1.414.
- The effective and average values of different waves are given below in tabular form.
- By phase of an alternating quantity is meant the fraction of time period of that alternating quantity that has elapsed since the quantity last passed through zero position of reference.
The angular displacement between the maximum positive values of two alternating quantities having the same frequency is called the phase difference between them.
An alternating quantity that attains its positive maximum value prior to the other is called the leading quantity.
An alternating quantity that attains its positive maximum value after the other is called the lagging quantity.
- The resultant current of two currents represented by
Following through a common conductor is given as
The sign of the phase angle ϕ of the resultant current will depend upon its position w.r.t. the reference phasor.