Alternating Current and emf

When a battery is connected to a circuit, it supplies current whose magnitude and direction remain constant. It is called a direct current. However, there is also a type of electric current whose magnitude and direction vary with time. Such current is known as alternating current (AC). A dynamo and electric generators at electric power plants produce ac.

Hence, the current or emf whose magnitude continuosly changes with time and direction reverses periodically is known as alternating current or emf. An alternating current reverses direction many times per second and has sinusoidal waveform. The circuits where an alternating source is applied are known as AC circuits.

Instantaneous Alternating Current and emf

The ac at any instant of time is called instantaneous ac. It is described as a sinusoidal current given by \[I=I_0\sin\omega t\text{ __(1)}\] The corresponding instantaneous emf is given by \[E=E_0\sin\omega t\text{ __(2)}\] where, $I_0$ is the maximum value of current called peak value of ac (or current amplitude) and $E_0$ is the maximum value of emf called peak value of alternating emf (or voltage amplitude).

$\omega$ is the angular frequency where $\omega$$=2πf$$=\frac{2π}{T}$, $f$ being the frequency of the source and $T$ is its time period. The value of $I$ and $E$ gives the instantaneous value of current and emf at an instant of time $t$.

Peak value

An ac varies periodically from zero to maximum in one direction and then from maximum to zero in other direction and so on. The maximum value of alternating current in either direction is called peak value of ac. It is denoted by $I_0$. Similarly, the maximum value of alternating emf in either direction is called peak value of alternating emf. It is denoted by $E_0$.

Time Period and Frequency

One complete set of positive and negative values of an alternating current or emf is known as a cycle. The time required to complete one cycle is called time period $(T)$. \[T=\frac{2π}{\omega}\] Frequency $(f)$ is the number of cycles per second given by \[f=\frac{1}{T}=\frac{\omega}{2π}\] where, $\omega$ is known as cycling frequency or angular frequency of ac. The unit of frequency is cycle per second which is called hertz $(\text{Hz)}$. \[\therefore 1\text{ Hz}=1\text{ cycle s}^{-1}\]

Sinusoidal Waveform of Alternating Current

The graphs of equations $\text{(1)}$ and $\text{(2)}$ are given below.

Sinusoidal Waveform of Alternating Current and emf

These graphs show sinusoidal curves. The alternating current and emf can also be represented in cosine function because cosine function also has the same waveform with constant phase difference.

Advantages of AC

  • AC is more economical to generate, transmit and distribute than DC. Sources of AC are easily available. Also, high voltage dc sources are not available whereas high voltage ac can be produced.
  • By using rectifiers, AC can be easily converted to DC.
  • AC can reach over long distances without much loss of power by using transformers. By using a transformer, alternating voltage can also be stepped down or stepped up easily.
  • AC can be controlled much better without any loss of electric power for example by using a choke coil.

Disadvantages of AC

  • AC can be more dangerous than DC because of its attractive nature and also its peak value is $\sqrt{2}$ times the rms value.
  • AC flows along the outer surface of the conducting wire which is called skin effect. This effect makes AC more dangerous. Hence, the transmission of ac requires several strands of thin wires insulated from each other, instead of a single thick wire.
  • AC can not be used in the electrolytic processes such as electroplating, electrotyping, refining, etc. For this purposes, only DC is used.

Next: Average or Mean Value of AC

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