When ac is driven through a capacitor and starts to increase (in either direction), it takes a fraction of a cycle for the voltage between the plates to follow. Once the current starts decreasing from its maximum peak (in either direction) in the cycle, it again takes a fraction of a cycle for the voltage to follow. The instantaneous voltage can’t quite keep up with the instantaneous current, as it does in a pure resistance. Thus, in a circuit containing capacitive reactance, the voltage lags the current in phase. Another, and more often used, way of saying this is that the current leads the voltage.
In a pure capacitive reactance, the current leads the voltage by 90°
Suppose an ac voltage source is connected across a capacitor. Imagine that the frequency is low enough, and/or the capacitance is small enough, so the absolute value of the capacitive reactance, XC, is extremely large compared with the resistance, R. Then the current leads the voltage by just about 90° (above figure).
The situation depicted in above figure represents a pure capacitive reactance. The vector in the RC plane in this situation points straight down. Its angle is −90° from the R axis.
Capacitance and Resistance
When the resistance in a resistance-capacitance circuit is significant compared with the absolute value of the capacitive reactance, the current leads the voltage by something less than 90° (below figure). If R is small compared with the absolute value of XC, the difference is almost a quarter of a cycle. As R gets larger, or as the absolute value of XC becomes smaller, the phase difference decreases. A circuit containing resistance and capacitance is called an RC circuit.
In a circuit with capacitive reactance and resistance, the current leads the voltage by less than 90°
The value of R in an RC circuit might increase relative to the absolute value of XC because resistance is deliberately put into a circuit. It can also happen if the frequency becomes so high that the absolute value of the capacitive reactance drops to a value comparable with the loss resistance in circuit conductors. In either case, the situation can be represented by a resistance, R, in series with a capacitive reactance, XC (following figure). If you know the values of XC and R, you can find the angle of lead, also called the RC phase angle, by plotting the point R − jXC on the RC plane, drawing the vector from the origin 0 − j 0 out to that point, and then measuring the angle of the vector clockwise from the R axis. You can use a protractor to measure this angle, as you did in the previous topics for RL phase angles. Or you can use trigonometry to calculate the angle.
Schematic representation of a circuit containing resistance and capacitive reactance.
As with RL circuits, you need only know the ratio of XC to R to determine the phase angle. For example, if XC = −4 Ω and R = 7 Ω, you’ll get the same angle as with XC = −400 Ω and R = 700 Ω, or with XC = −16 Ω and R = 28 Ω. The phase angle will be the same whenever the ratio of XC to R is equal to −4:7.
As the resistance in an RC circuit gets large compared with the absolute value of the capacitive reactance, the angle of lead becomes smaller. The same thing happens if the absolute value of XC gets small compared with the value of R.
When R is many times larger than the absolute value of XC, whatever their actual values, the vector in the RC plane points almost along the R axis. Then the RC phase angle is close to 0°. The voltage comes nearly into phase with the current. The plates of the capacitor do not come anywhere near getting fully charged with each cycle. The capacitor is said to “pass the ac” with very little loss, as if it were shorted out. But it will still have an extremely high XC for any ac signals at much lower frequencies that might exist across it at the same time. (This property of capacitors can be put to use in electronic circuits. An example is when an engineer wants to let radio-frequency signals get through while blocking signals at audio frequencies.)
Ultimately, if the absolute value of the capacitive reactance gets small enough, the circuit acts as a pure resistance, and the current is in phase with the voltage.