Electrostatics - Alternating Current

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Alternating Current

The primary source of in such circuits is a battery and the basic circuit element is an ohmic resistance (R) which controls the current (I) as per ohm’s law 

V = IR

But most of the electric power generated and used in the worlds is the form of automating current. This is because 
    
Alternating voltages can be easily and efficiently converted from one value to the other by means of transformers. 
    
The alternating current energy can be transmitted and distributed over long distance economically without much loss of energy.
    
The magnitude of alternating current changes continuously with time and its direction is reversed periodically. It is represented by 

I = I₀ sin w I  

Or

I = I₀ cos w I

Here I is instantaneous value of current magnitude of current at any instant of time t and I0 is the peak value or maximum value of A.C. it is also called amplitude of A.C. w is called angular frequency of A.C.

Also W = 2π/T = 2πv

Where T is the time period or period of it is equal to the time taken by the to go through one complete cycle of variation (zero to maximum, maximum to zero: zero to maximum in opposite direction and finally max to zero). Again v is the frequency of it is equal to the number of complete cycles of variation gone through by the in one second.

We have shown A.C. as sine function of the time periods of the two wave forms are indicated as T and Tand their frequencies are v and v respectively. Form these figures we find

T = 2T and v = 2v 
 
The terms used of hold equally for alternating which may be represented by 

E = E₀ sin w t 

Or 

E = E₀ cos w t

In circuits two additional circuit elements are used these are inductor (L) and capacitor (C) thus current and voltage in circuits are controlled by three circuit elements R, L and C.

The voltage V across a pure inductor L is given by V = L (dI/dt)

Where dI/dt is rate of change of current,

For an ideal capacitor of capacitance C the corresponding relation is 

I = C dV/ dt

(∴ I = dQ / dt and Q = CV), where dV/dt is rate of change of potential.

An inductor affects the voltage only when current I changes with time. Shows that a capacitor affects the current only when V changes with time V and I must be time dependent in sake of L and C but this is not the requirement in case of resistors R 

In this aspect we shall consider two kinds of time varying voltages and current. Firstly when a circuit is switched on an off we shall show that current does not rise or fall instantly. The growth and decay of current are gradual with characteristic time called time constant of the circuit. Secondly we shall discuss the behaviour of the circuit elements R, L and C towards voltages varying as sine function or cosine function of time.  

 

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