12.1 Alternating current, inductance and capacitance

When the frequency is high, the capacitive reactance is low. This is why a capacitor allows the flow of high frequency AC because its reactance decreases with increasing frequency.

Inductance

Inductance (measured in henries, symbol H) is a measure of the generated emf for a unit change in current. For example, an inductor with an inductance of 1 H produces an emf of 1 V when the current through the inductor changes at the rate of 1 A $·$ s ${}^{-1}$ .

An inductor is a passive electrical device used in electrical circuits for its property of inductance. An inductor is usually made as a coil (or solenoid) of conducting material, typically copper wire, wrapped around a core either of air or of ferromagnetic material.

Electrical current through the conductor creates a magnetic flux proportional to the current. A change in this current creates a change in magnetic flux that, in turn, generates an emf that acts to oppose this change in current.

The inductance of an inductor is determined by several factors:

• the shape of the coil; a short, fat coil has a higher inductance than one that is thin and tall.
• the material that the conductor is wrapped around.
• how the conductor is wound; winding in opposite directions will cancel out the inductance effect, and you will have only a resistor.

The inductance of a solenoid is defined by:

where ${\mu }_0$ is the permeability of the core material (in this case air), $A$ is the cross-sectional area of the solenoid, $N$ is the number of turns and $l$ is the length of the solenoid.

Permeability

Permeability is the property of a material which describes the magnetisation developed in that material when excited by a source.

An inductor in an AC circuit also has a reactance, $X_L$ . Reactance is the property of an inductor that opposes the flow of AC current. Reactance is defined by:

where $L$ is the inductance and $f$ is the frequency of the AC.

If we examine the equation for the reactance of an inductor, we see that inductive reactance increases with increasing frequency. Therefore, when the frequency is low, the inductive reactance is very low. This is why an inductor allows the flow of DC and low frequency AC because its reactance decreases with decreasing frequency.

When the frequency is high, the inductive reactance is high. This is why an inductor blocks the flow of high frequency AC because its reactance increases with increasing frequency.

Exercise - capacitance and inductance

1. Describe what is meant by reactance.
2. Define the reactance of a capacitor.
3. Explain how a capacitor blocks the flow of DC and low frequency AC but allows the flow of high frequency AC.
4. Describe what is an inductor.
5. Describe what is inductance.
6. What is the unit of inductance?
7. Define the reactance of an inductor.
8. Write the equation describing the inductance of a solenoid.
9. Explain how an inductor blocks high frequency AC, but allows low frequency AC and DC to pass.

Summary

1. Electrical generators convert mechanical energy into electrical energy.
2. Electric motors convert electrical energy into mechanical energy.
3. There are two types of generators - AC and DC. An AC generator is also called an alternator.
4. There are two types of motors - AC and DC.
5. Alternating current (AC) has many advantages over direct current (DC).
6. Capacitors and inductors are important components in an AC circuit.
7. The reactance of a capacitor or inductor is affected by the frequency of the AC.

End of chapter exercise

1. [SC 2003/11] Explain the difference between alternating current (AC) and direct current (DC).
2. Explain how an AC generator works. You may use sketches to support your answer.
3. What are the advantages of using an AC motor rather than a DC motor.
4. Explain how a DC motor works.
5. At what frequency is AC generated by Eskom in South Africa?
6. IEB 2001/11 HG1 - Work, Energy and Power in Electric Circuits Mr. Smith read through the agreement with Eskom (the electricity provider). He found out that alternating current is supplied to his house at a frequency of 50 Hz. He then consulted a book on electric current, and discovered that alternating current moves to and fro in the conductor. So he refused to pay his Eskom bill on the grounds that every electron that entered his house would leave his house again, so therefore Eskom had supplied him with nothing! Was Mr. Smith correct? Or has he misunderstood something about what he is paying for? Explain your answer briefly.
7. What do we mean by the following terms in electrodynamics?
   1. inductance
   2. reactance
   3. solenoid
   4. permeability