[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*}
\(\text{20,38} \times \text{10}^{\text{6}}\) \(\text{W}\)