Alternating currents      

The p.d. across the resistor at time t is given by 

V = V_o sin wt     where V_o = the peak voltage

                               w = the angular frequency

The corresponding alternating current, I , is

I = I_o sin wt

Root-mean-square values :      and

The above two formulae are true only for sin wt or cos wt alternating voltage or current

 A.C. through a pure capacitance   :

the p.d. across the capacitor at time t is given by

                V = V _o sin wt

Q = C V = C V_o sin wt           and      where I_o = CV_o w

In a purely capacitative circuit the current leads the applied p.d. by π/2 radians.

 Capacitative reactance X_C :         

A.C. through a pure inductance     :

An alternating current ( I = I_o sin wt ) flows through the inductor and sets up a changing magnetic flux.

V= I_o wL cos wt = V_o cos wt  = V_o sin (wt + π/2  )   and X_C = w L

In a purely inductive circuit the applied p.d. leads the current by π/2 radians.

 Resistance and inductance in series circuit : 

 Resistance, capacitance and inductance in series circuit :        

resonant frequency : 

Power in a.c. circuits

(a)   Resistance         : 

The mean power =

(b)    Inductance        :  

The instantaneous power= (I_o sin wt) (V_o sin(wt+π)

 The mean power =       

 (c)       Capacitance   :

The instantaneous power = ( I_o sin (wt + π/2) ) ( V_o sin wt )

The mean power =  = 0

(d)   Formula for a.c. power :     

The mean power =