Alternating Current Revision Notes for Grade 12 NSC Matric Physical Sciences

Alternating Current

What is alternating current?

When you first learn about electricity, you typically start with direct current (DC), which flows in only one direction. This is the type of electricity produced by batteries, where there are clear positive and negative terminals.

However, the electricity generated by power stations works differently. This electricity constantly alternates or switches direction, which is why it's called alternating current (AC). In South Africa, this alternating happens at a frequency of 50 Hz, meaning the current changes direction 50 times every second.

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The circuit symbol for alternating current consists of a circle with a wavy line inside it, representing the alternating nature of the current.

Advantages of AC over DC

AC has several important advantages over DC that make it the preferred choice for electrical power distribution:

Easy transformation - AC voltage can be easily stepped up or stepped down using transformers
Efficient transmission - AC can be transmitted at high voltage and low current over long distances with minimal energy loss due to heating
Simple voltage conversion - It's easier to convert from AC to DC than from DC to AC
Easy generation - AC is easier to generate than DC using rotating generators
Motor applications - High frequency AC is particularly suitable for electric motors

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These advantages make AC the universal choice for power grid systems worldwide. The ability to easily transform voltage levels allows power companies to transmit electricity efficiently over long distances and then step it down to safe levels for household use.

Current and voltage in AC circuits

In a DC circuit, current and voltage remain constant over time. However, in an AC circuit, both current and voltage vary continuously with time. The value of current or voltage at any specific moment is called the instantaneous current or instantaneous voltage.

These values follow sinusoidal patterns and can be calculated using these equations:

$i = I_{max} \sin(\omega t)$

$v = V_{max} \sin(\omega t)$

Where:

$i$ = instantaneous current
$I_{max}$ = maximum current
$v$ = instantaneous voltage
$V_{max}$ = maximum voltage
$f$ = frequency of the AC
$t$ = time at which the calculation is made

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The sinusoidal nature of AC means that both current and voltage smoothly vary between positive and negative peak values, creating the characteristic wave pattern that defines alternating current.

RMS (root mean square) values

Since AC current and voltage are constantly changing, we need a way to express their effective values. The root mean square (RMS) value represents the equivalent DC value that would produce the same power output.

RMS values are calculated using these formulas:

$I_{rms} = \frac{I_{max}}{\sqrt{2}}$

$V_{rms} = \frac{V_{max}}{\sqrt{2}}$

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The RMS value is crucial because AC varies sinusoidally - it's equally positive and negative. If we calculated a simple average, we'd get zero. The RMS value solves this problem by giving us a meaningful measure of AC's effective strength.

Power in AC circuits

In circuits containing only resistive components, the average power can be calculated using RMS values:

$P_{av} = I_{rms} \times V_{rms}$

This can also be expressed as:

$P_{av} = \frac{I_{max} \times V_{max}}{2}$

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An important point about AC power: since both current and voltage have the same sign at any given moment (both positive or both negative), the power is always positive. This means the average power won't be zero, unlike the case with current or voltage alone in AC circuits.

Worked example 1: Laptop transformer calculations

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Worked Example: Laptop Transformer Calculations

Question: A laptop transformer has the following specifications:

INPUT: 100-240 V; 1,5 A; 50/60 Hz
OUTPUT: 20 V; 3,25 A

Calculate the RMS current and voltage values for a 240 V input.

Solution:

Step 1: Identify what changes from input to output The input includes frequency because it's designed for AC household use. The output has no frequency listed, meaning it produces DC output.

Step 2: Calculate RMS values for the input Since the transformer takes AC input, we only need RMS values for the input:

$V_{rms} = \frac{V_{max}}{\sqrt{2}} = \frac{240}{\sqrt{2}} = 169.71 \text{ V}$

$I_{rms} = \frac{I_{max}}{\sqrt{2}} = \frac{1.5}{\sqrt{2}} = 1.06 \text{ A}$

Worked example 2: Camera battery charger

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Worked Example: Camera Battery Charger

Question: A camera charger shows:

INPUT: 100-240 V; 0,085 A (100 V) - 0,05 A (240 V); 50/60 Hz
OUTPUT: 4,2 V; 0,7 A

Calculate RMS values for both input voltages.

Solution:

For 100 V input: $V_{rms} = \frac{100}{\sqrt{2}} = 70.71 \text{ V}$ $I_{rms} = \frac{0.085}{\sqrt{2}} = 0.06 \text{ A}$

For 240 V input: $V_{rms} = \frac{240}{\sqrt{2}} = 169.71 \text{ V}$ $I_{rms} = \frac{0.05}{\sqrt{2}} = 0.035 \text{ A}$

Worked example 3: Power calculation

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Worked Example: Power Calculation

Question: Using the laptop transformer from Example 1 (240 V input), calculate the average power dissipated.

Solution:

Step 1: Use previously calculated RMS values $V_{rms} = 169.71$ V
$I_{rms} = 1.06$ A

Step 2: Calculate average power $P_{av} = I_{rms} \times V_{rms} = 1.06 \times 169.71 = 179.89 \text{ W}$

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Key Points to Remember:

AC constantly changes direction while DC flows in one direction only
South Africa uses 50 Hz frequency for AC power generation
RMS values equal maximum values divided by √2 - this gives the effective AC value
AC can be easily transformed using transformers, making it ideal for power transmission
Power in AC circuits is always positive because current and voltage have the same sign at any moment

Alternating Current (Grade 12 NSC Matric Physical Sciences): Revision Notes