AC circuit containing only a capacitor
Consider a circuit containing a capacitor of capacitance C connected across an alternating voltage source (Figure 4.49). The alternating voltage is given by
Let q be the instantaneous charge on the capacitor. The emf across the capacitor at that instant is q/C According to Kirchoff’s loop rule,
By the definition of current,
Instantaneous value of current,
where [Vm] / [1/Cω] = Im , the peak value of the alternating current. From equations (4.49) and (4.50), it is clear that current leads the applied voltage by π/2 in a capacitive circuit. This is shown pictorially in Figure 4.50. The wave diagram for a capacitive circuit also shows that the current leads the applied voltage by 90º.
The peak value of current Im is given by Im = [Vm] / [1/Cω]. . Let us compare this equation with Im = Vm/R from resistive circuit. The quantity 1/ Cω plays the same role as the resistance R in resistive circuit. This is the resistance offered by the capacitor, called capacitive reactance (XC). It measured in ohm.
The capacitive reactance (XC) varies inversely as the frequency. For a steady current, f = 0.
Thus a capacitive circuit offers infinite resistance to the steady current. So that steady current cannot flow through the capacitor.
A capacitor of capacitance 102/π µF is connected across a 220 V, 50 Hz A.C. mains. Calculate the capacitive reactance, RMS value of current and write down the equations of voltage and current.