AC Electrics - Introduction to AC

Inductive Reactance

The opposition to current flow in this circuit is called the Inductive Reactance.

It is called reactance rather than resistance because the effects of inductance depend on the frequency of the supply as well as the value of the inductance.

Inductive reactance is measured in ohms and is given the symbol XL.

To determine inductive reactance the following formula can be used.

XL = 2 π f L

where π is a constant, f is the frequency, L is the inductance

From this formula it can be seen that as frequency increases, the value of inductive reactance increases so the circuit current would decrease. Conversely, and more importantly, as the circuit frequency decreases, the inductive reactance decreases and the circuit current increases.

Capacitance in AC Circuits

Capacitance is the ability of a circuit to store an electrical charge. A device used to introduce capacitance into a circuit is known as a Capacitor. A capacitor consists of two plates separated by a dielectric, see Figure 11.10. Dielectrics can be, amongst other things, air, mica or waxed paper.

Three factors affect the amount of charge a capacitor can hold.

They are:

•The area of the plates.

•The distance between the plates.

•The material used to separate the plates, the dielectric.

The capacitor will store an electric charge, much like a hydraulic accumulator stores fluid under pressure, but first it needs to be charged.

When connected to the battery as shown in Figure 11.10 electrons will be removed from the plate connected to the positive terminal of the battery and added to the plate connected to the negative terminal, conventional current flow will be from positive to negative. This process will continue until the plates become saturated and no more current will flow.

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AC Electrics - Introduction to AC 11

AC to Introduction - Electrics AC 11

Figure 11.10 A capacitor in a DC circuit

The potential difference between the plates is at its maximum and the capacitor is now fully charged, its voltage being equal to the battery voltage.

If the switch is now moved to a mid position, the charging circuit is disconnected and the capacitor will hold its charge indefinitely, in a similar fashion to an accumulator. (In practice there will be some leakage which allows the capacitor to discharge over a period of time).

Using the switch to connect the capacitor to the external circuit will allow the capacitor to discharge and current will flow around the circuit in the opposite direction until the potential difference across the plates has become equal. Notice that the capacitor has discharged in the opposite direction to which it was charged. Note also that electrons do not pass between the plates through the dielectric

Figure 11.11 Capacitor in an AC circuit.

When fitted in an AC circuit as shown in Figure 11.11 the capacitor will be constantly charging and discharging as the applied voltage and current flow are constantly reversing polarity and direction. As the applied voltage falls, the capacitor discharges current back into the circuit in the opposite direction and its voltage falls.

This has the effect of shifting the voltage out of phase with the current, and in a purely capacitive circuit the current will lead the voltage by 90°. See Figure 11.12.

The unit of capacitance is the farad, and a capacitor is given the symbol C. If a current of 1 ampere flowing for 1 second creates a potential difference of 1 volt between the plates of a capacitor then it is a 1 farad capacitor. Because of the values involved, a 1 farad capacitor is not a practical size and a more common unit is the microfarad or picofarad.

Figure 11.12 Phase relationship in a purely capacitive circuit

Capacitive Reactance

The opposition to current flow in this circuit is called Capacitive Reactance. As in the inductive circuit, the amount of reactance is dependent upon frequency and the value of the capacitor in farads. Capacitive reactance is measured in ohms and is given the symbol XC. It can be calculated by using the following formula:

From this formula it can be seen that as frequency increases, the value of capacitive reactance decreases so the circuit current will increase. Conversely if frequency decreases, capacitive reactance increases and circuit current will decrease.

AC Electrics - Introduction to AC 11

AC to Introduction - Electrics AC 11

The total opposition to current flow in an AC circuit is a combination of resistance, inductive reactance and capacitive reactance. But because in each circuit there is a different phase relationship between the voltage and current, they cannot simply be added together.

Inductive reactance can be thought of as having the opposite effect to capacitive reactance as in one circuit the current lags the voltage by 90° and in the other the current leads the voltage by 90°, so they are 180° apart and the total reactance can be found by subtracting one from the other. Impedance is the vector sum of the resistance and total reactance and represents the total opposition to current flow measured in ohms and given the symbol Z.

Figure 11.13

Pictorially this can be shown as vectors in an impedance triangle, from which it can be seen that resistance is out of phase with reactance by 90°:

Mathematically the vector sum of the two can be expressed using Pythagoras’ Theorem.

Resonant Circuits

Changes of supply frequency in a circuit will have the opposite effect on capacitance and inductance. An increase of supply frequency will increase the inductive reactance (XL) and decrease the capacitive reactance (XC). Increasing XL will cause the current in the circuit to decrease and decreasing XC will cause the current to increase.

The manner in which the inductance and capacitance react in an opposite way to changes of supply frequency means that there will be one specific frequency for each circuit at which their values will be equal.

When the Capacitive Reactance and the Inductive Reactance in a circuit are equal the circuit is said to be Resonant.

If a capacitor and an inductance are placed in series with each other, at the resonant frequency the current flowing in the circuit will be maximum. If, on the other hand, the capacitor and inductance are placed in parallel with each other, the current flowing in the circuit at resonant frequency will be at a minimum.