Alternating Current and voltage

AC Current

An alternating current is that which flows first in one direction in a circuit, which is called positive direction, then  flow in reverse direction which is called negative direction ,repeating such cycle of changes continuously.

The graph to a base of time shows the waveform of the current as a succession of instantaneous values.

Graph of alternating current and voltage

In general there will be peak values in both positive and negative half cycles where the current is momentarily greatest.

Time period

The time occupied by one complete cycle is called the period


The number of cycle completed in one second is called frequency in cycle per second or Hertz ( Hz ).

An alternating voltage produced alternating current. The alternating voltage and current may or may not be in phase.If it is not in phase then they are said to have phase difference .

The term phase difference is only meaningful only in case of alternating quantities and harmonically varying function of the time.

The phase difference may be indicated by a time interval between the zeros of the voltage and current waves at the beginning of a positive half cycle.

alternating current equation

The instantaneous value of alternating current is given by

alternating current equation

If T is the time period of alternating current and f its frequency then

Frequency equation

Instantaneous value of alternating current can be represented by sine equation or cosine equation. Both representation lead to the same result.

Similarly instantaneous value of alternating e.m.f may be represented by

emf  Equation for AC

Since alternating current varies continuously with time ,its effect is measured either by mean value ( or average value )of a.c or by defining root mean square value ( or virtual value ) of A.C current

Average and RMS value

Mean or average value of AC;

The steady or direct current which transfer in the circuit the same charge as a transferred by the ac during the alternation is called the mean or average value of alternating wave.

The ac voltage or current at any time is given by

ac voltage equation

where w is called angular frequency of AC.

Relation Between mean value and peak value

Relation between peak value and rms

RMS Value of AC

The RMS value of an alternating current is the value of direct current which produced in the same conductor the same amount of heat in the same time.

R.M.S Value of A.C current=Virtual value =Effective current


Relation between virtual value and peak value of a.c

virtual vs peak value

The R.M.S or virtual value of ac is same even for a complete cycle of ac

This fact fact is made use of to construct hot wire instruments for measuring current and voltages.Such ammeter and voltmeter record virtual value of alternating current and voltage

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