An a.c. circuit, when contains only a capacitor or a condenser, has capacitance only. Such a circuit is shown in fig 31(a).
As inductance causes a voltage drop across it and an angle of phase difference between applied voltage and the circuit current, so does the capacitance. Capacitance, in conjunction with supply frequency, offers an opposition to the flow of current through the circuit. This opposition is known as Capacitive Reactance of the capacitor. It is usually denoted by XC and is expressed in ohm. If the capacitance of the capacitor be C farad and the supply frequency be f hertz, capacitive reactance,
XC = 1/2πfc ohm.
Capacitive reactance causes a voltage drop across the capacitor. If V be the voltage across the capacitor and I be the current in ampere flowing through it, then,
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V = IXC volt, or f = V/XC ampere.
Capacitance always works in opposition to inductance. While inductance makes the current lagging behind the applied voltage by 90°, Capacitance makes the current leading the voltage by 90°. This is shown in fig. 31(b) and 31(c).
When a capacitor is uncharged, there is no potential difference between its two plates. At this stage if supply is given to the capacitor, maximum current will flow through it. Thus, current is maximum when voltage is zero. As the current flows through the capacitor, electro-static charge is accumulated in it and the potential difference between the plates rises.
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During this time current gradually decreases and finally ceases to flow when the potential difference between the plates becomes equal and opposite to supply voltage, i.e., when the potential difference is maximum. It is therefore evident that the charging current of a Capacitor leads the potential difference across the plates by 90°.
Power absorbed by a Capacitor:
As the current is alternating, a capacitor connected in an a.c. circuit is alternately charged and discharged. For quarter cycle a capacitor is gradually charged when it draws energy from the supply line. This energy is stored in the electro-static field produced by the capacitor.
For the next quarter cycle the capacitor is gradually discharged. During this time the electro-static field collapses and the stored energy flows back to the supply line. Hence, the average power absorbed by a capacitor is nil. Like inductance, therefore, capacitance also does not do any useful work in the circuit.
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Example:
A Capacitor of Capacitance 20 micro-farad is connected to 550-volt, 50-hz supply. Find the reactance of this capacitor and the current flowing through it.
Solution:
