same as that of resistance and its SI unit is ohm ( Ω ). The capacitive reactance limits the amplitude of the current in a purely capacitive circuit in the same way as the resistance limits the current in a purely resistive circuit. But it is inversely proportional to the frequency and the capacitance. A comparison of Eq.
( . ) with the equation of source voltage, Eq. ( . ) shows that the current is π / ahead of voltage.
Figure . (a) shows the phasor diagram at an instant t . Here the current phasor I is π / ahead of the voltage phasor V as they rotate counterclockwise. Figure .
(b) shows the variation of voltage and current with time. We see that the current reaches its maximum value earlier than the voltage by one-fourth of a period. The instantaneous power supplied to the capacitor is p c = i v = i m cos( ω t ) v m sin( ω t ) = i m v m cos( ω t ) sin( ω t ) sin( i v ( . ) So, as in the case of an inductor, the average power sin( sin( i v i v P since <sin ( ω t )> = over a complete cycle.
Figure . explains it in detail. Thus, we see that in the case of an inductor, the current lags the voltage by π / and in the case of a capacitor, the current leads the voltage by π / . Example .
A lamp is connected in series with a capacitor. Predict your observations for dc and ac connections. What happens in each case if the capacitance of the capacitor is reduced? Solution When a dc source is connected to a capacitor, the capacitor gets charged and after charging no current flows in the circuit and the lamp will not glow.
There will be no change even if C is reduced. With ac source, the capacitor offers capacitative reactance ( / ω C ) and the current flows in the circuit. Consequently, the lamp will shine. Reducing C will increase reactance and the