Alternating current(AC) through Capacitor

AC through pure capacitor

  • Figure given below shows circuit containing alternating voltage source
    connected to a capacitor of capacitance C

    AC through pure capacitor

  • Suppose at any time t,q be the charge on the capacitor and i be the current in the circuit
  • Since there is no resistance in the circuit, so the instantaneous potential drop q/C across the capacitor must be equal to applied alternating voltage
  • Since i=dq/dt is the instantaneous current in the circuit so

    is the peak value of current
  • Comparing equation (13) with V=V0sinωt ,we see that in a perfect capacitor current leads emf by a phase angle of π/2
  • This phase relationship is graphically shown below in the figure

    Sinusodical representation of relationship between current and voltage in capacitor circuit

  • Again comparing peak value of current with ohm's law ,we find that quantity 1/ωC has the dimension of the resistance
  • Thus the quantity
    XC=1/ωC =1/2πfC ---(14)
    is known as capacitive reactance
  • From equation (14) we see that capacitive reactance decreases with increasing frequency of current and in infinite for direct current for which frequency f=0