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End of chapter exercises

Textbook Exercise 11.3

[SC 2003/11] Explain the difference between alternating current (AC) and direct current (DC).

Direct current (DC), which is electricity flowing in a constant direction. DC is the kind of electricity made by a battery, with definite positive and negative terminals. However, we have seen that the electricity produced by some generators alternates and is therefore known as alternating current (AC). So the main difference is that in AC the movement of electric charge periodically reverses direction while in DC the flow of electric charge is only in one direction.

Explain how an AC generator works. You may use sketches to support your answer.

Solution not yet available

What are the advantages of using an AC motor rather than a DC motor.

While DC motors need brushes to make electrical contact with moving coils of wire, AC motors do not. The problems involved with making and breaking electrical contact with a moving coil are sparking and heat, especially if the motor is turning at high speed. If the atmosphere surrounding the machine contains flammable or explosive vapours, the practical problems of spark-producing brush contacts are even greater.

Explain how a DC motor works.

Instead of rotating the loops through a magnetic field to create electricity, as is done in a generator, a current is sent through the wires, creating electromagnets. The outer magnets will then repel the electromagnets and rotate the shaft as an electric motor. If the current is DC, split-ring commutators are required to create a DC motor.

At what frequency is AC generated by Eskom in South Africa?

In South Africa the frequency is \(\text{50}\) \(\text{Hz}\)

(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 \(\text{50}\) \(\text{Hz}\). 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.

Mr Smith is not correct. He has misunderstood what power is and what Eskom is charging him for.

AC voltage and current can be described as: \begin{align*} i &= I_{\max} \sin(2\pi ft + \phi)\\ v &= V_{\max} \sin(2\pi ft) \end{align*} This means that for \(\phi = 0\), i.e. if resistances have no complex component or if a student uses a standard resistor, the voltage and current waveforms are in-sync.

Power can be calculated as \(P = VI\). If there is no phase shift, i.e. if resistances have no complex component or if a student uses a standard resistor then power is always positive since:

  • when the voltage is negative (−), the current is negative (−), resulting in positive (+) power.
  • when the voltage is positive (+), the current is positive (+), resulting in positive (+) power.

You are building a laser that takes alternating current and it requires a very high peak voltage of \(\text{180}\) \(\text{kV}\). By your calculations the entire laser setup can be treated at a single resistor with an equivalent resistance of \(\text{795}\) \(\text{ohms}\). What is the rms value for the voltage and the current and what is the average power that your laser is dissipating?

At peak voltage the peak current will be:

\begin{align*} V&=IR \\ I&=\frac{V}{R} \\ &=\frac{\text{180} \times \text{10}^{\text{3}}}{795} \\ &= \text{226,415094}\ldots \\ &\approx \text{226,42}\text{ A} \end{align*} \begin{align*} P_{rms}&= V_{rms}I_{rms} \\ &= \left(\frac{\text{180} \times \text{10}^{\text{3}}}{\sqrt{2}}\right) \left(\frac{\text{226,415094}\ldots}{\sqrt{2}}\right) \\ &= \text{20,37735}\ldots \times \text{10}^{\text{6}} \\ &\approx \text{20,38} \times \text{10}^{\text{6}}\text{ W} \end{align*} \(\text{20,38} \times \text{10}^{\text{6}}\) \(\text{W}\)