Alternating Current (A.C)

Alternating Current (A.C)




Fig.


An alternating current is one which changes in magnitude and direction periodically. It is represented by a 'sine' or cosine function.

The value of current at any time 't' is given by i = i_osin t.

where i_o is maximum current (amplitude) and w is angular frequency.

AC voltage can also be represented by a 'sine' function. E = E_osin t.

Instantaneous value of ac is the strength of electric current at any instant. Peak or maximum value of ac is the maximum current is the cycle. Mean or average

of ac is equal to dc which transforms same charge across the circuit as that of ac during the same time.

across the circuit i_av= i_max



Different AC Circuit

AC Through a Resistor

If I = I₀sin t, then

E = E₀sin t





AC Through an Inductor

If E = E₀sin t

I = I₀sin (t - /2)




The phase or diagram is shown below:



X_L= L = 2pf L, where f is frequency of AC

X_Lis measured in ohm

The variation of X_Lwith f is shown in fig.




AC Through a Capacitor

If E = E₀sin t

I = I₀sin (t + /2)



The variation of E and I with wt is shown below. In this representation,

E = E₀sin t and I = I₀sin





AC Through LR Circuit

(i) If I = I₀sin wt, then

E = E₀sin (t + )



(ii) Inductive Impedance

Z_L=

The reciprocal of impedance is called admittance.

(iii) Power in LR Circuit Average power, P_av= E_vI_v


AC Through CR Circuit

(i) If E = E₀sin wt, then

I = I₀sin (t + )



(ii) Capacitive Impedance

Z_C=


AC Through LCR Circuit

If I = I₀sin t, then

E = E₀sin (t + )