Consider a circuit containing a capacitor of capacitance C connected across an alternating voltage source.

**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 Kirchoffâ€™s loop rule,

By the definition of
current,

Instantaneous value of
current,

where [V_{m}] /
[1/CÏ‰] = I_{m} , the peak value of the alternating current. From equations (4.49) and
(4.50), it is clear that current leads the applied voltage by Ï€/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 90Âº.

**Capacitive reactance X**_{C}

The peak value of
current *I*_{m} is given by I_{m} = [V_{m}] /
[1/CÏ‰]. . Let us compare this equation
with Im = V_{m}/R from resistive circuit. The quantity 1/ CÏ‰ plays the same role as the resistance R in
resistive circuit. This is the resistance offered by the capacitor, called capacitive reactance (*X*_{C}).
It measured in ohm.

The capacitive reactance
(*X*_{C}) 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.

** **

** **

**EXAMPLE 4.21**

A capacitor of
capacitance 10^{2}/Ï€ ÂµF 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.

**Solution**

Tags : Phasor diagram, Circuit Diagram, Formula, Solved Example Problems | Alternating Current (AC) , 12th Physics : Electromagnetic Induction and Alternating Current

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12th Physics : Electromagnetic Induction and Alternating Current : AC circuit containing only a capacitor | Phasor diagram, Circuit Diagram, Formula, Solved Example Problems | Alternating Current (AC)