Home : Book details : Book description

Description of  Alternating Current-AC: Physics of Alternating Current (A.C.) (Learn Physics Book 26)

Alternating Quantities (i or V) (1) An alternating quantity (current i or voltage V) is one whose magnitude changes continuously with time between zero and a maximum value and whose direction reverses periodically. (2) Some graphical representation for alternating quantities (3) Equation for i and V : When a coil is rotated rapidly in a strong magnetic field, magnetic flux linked with the coil changes. As a result an emf is induced in the coil and induced current flows through the circuit. These voltage and current are known as alternating voltage and current Equation: Alternating current or voltage varying as sine function can be written as i = i0 sint = i0 sin 2 t = i0sin and where i and V are Instantaneous values of current and voltage, i0 and V0 are peak values of current and voltage = Angular frequency in rad/sec, = Frequency in Hz and T = time period About Cycle (i) The time taken to complete one cycle of variations is called the periodic time or time period. (ii) Alternating quantity is positive for half the cycle and negative for the rest half. Hence average value of alternating quantity (i or V) over a complete cycle is zero. Area under the positive half cycle is equal to area under negative cycle. (iii) The value of alternating quantity is zero or maximum 2 times every second. The direction also changes 2 times every second. (iv) Generally sinusoidal waveform is used as alternating current/voltage. (v) At from the beginning, i or V reaches to their maximum value. Note : If instantaneous current i (or voltage V) becomes 1/n times of it's peak value in time t then second. Important Values of Alternating Quantities (1) Peak value (i0 or V0) : The maximum value of alternating quantity (i or V) is defined as peak value or amplitude. (2) Mean square value : The average of square of instantaneous values in one cycle is called mean square value. It is always positive for one complete cycle. e.g. or (3) Root mean square (r.m.s.) value : Root of mean of square of voltage or current in an ac circuit for one complete cycle is called r.m.s. value. It is denoted by Vrms or irms = 0.707 i0 = 70.7% i0 Similarly of V0 (i) The r.m.s. value of alternating current is also called virtual value or effective value. (ii) In general when values of voltage or current for alternating circuits are given, these are r.m.s. value. (iii) ac ammeter and voltmeter are always measure r.m.s. value. Values printed on ac circuits are r.m.s. values. (iv) In our houses ac is supplied at 220 V, which is the r.m.s. value of voltage. It's peak value is (v) r.m.s. value of ac is equal to that value of dc, which when passed through a resistance for a given time will produce the same amount of heat as produced by the alternating current when passed through the same resistance for same time. Note : r.m.s. value of a complex current wave (e.g. i = a sin t + b cos t) is equal to the square root of the sum of the squares of the r.m.s. values of it's individual components i.e. . (4) Mean or Average value (iav or Vav) : The average value of alternating quantity for one complete cycle is zero. The average value of ac over half cycle (t = 0 to T/2) of i0, Similarly of V0.