17.1 Alternating Current and its Characteristics

17.1 Alternating Current and its Characteristics

An alternating current AC means a sinusoidally varying current which can be represented by time dependent sine or cosine functions. The emf of an AC generator is given by the following equation, for voltage:

where $V$ represents magnitude of alternating current or voltage corresponding to time $t$, $V_{o}$ represents maximum value of voltage and $\omega$ is the angular frequency of alternating voltage as shown in Fig 17.1. We can write Eq. 17.1 for current as: $I = I_{o} \sin \omega t$ where $I$ is instantaneous value of alternating current at time $t$, $I_{o}$ is its maximum or peak value $\omega$ is its angular frequency.

A periodically varying current or voltage is termed as alternating if every cycle corresponds to one time period ($T$) with two exactly symmetrical half cycles having one half is positive and remaining half is negative. In case of current, the direction of current reverses after every half-cycle and in case of voltages, the polarity of potential difference reverses after every half cycle. The second condition to be an alternating one is that amplitude or the peak value of current or voltage i.e., the maximum value on both positive and negative sides remains constant in all cycles but changes occur most rapidly at the zero (crossover) points and most slowly at its peak (Fig. 17.1).

(Fig. 17.1: Waveform of alternating voltage)

Some important terms related to alternating quantities are:

Waveform: The path traced by an alternating quantity, such as the voltage in Fig. 17.1 plotted as a function of some variable such as time.

Cycle: One complete set of positive and negative values of an alternating quantity is called a cycle. Figure 17.1 shows one cycle of an alternating voltage.

Time period ($T$): The time taken to complete one cycle of an alternating quantity is called its time period and is measured in seconds.

Frequency ($f$): The number of cycles that occur in one second is called its frequency. The unit of frequency is hertz ($\mathrm{Hz}$); where $1\,\mathrm{Hz} = 1$ cycle per second and $f = 1/T$.

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Why is AC better than DC? AC is easy to be transferred over longer distances even between two cities without much energy loss. DC cannot be transferred over a very long distance. It loses electric power.