Introduction to Alternating Currents and Transformers

Welcome to one of the most practical chapters in your Physics A-level! So far, you have likely spent a lot of time looking at Direct Current (DC)—the kind of electricity you get from a battery where the charge flows in one direction only. In this chapter, we explore Alternating Current (AC), where the current constantly flips direction. This is the electricity that powers your home and the entire National Grid. We will also look at transformers, the clever devices that allow us to change voltages so we can move electricity across the country without losing too much energy.

1. Understanding Alternating Current (AC)

In an AC circuit, the potential difference (pd) and current follow a sinusoidal pattern. This means they vary like a sine wave over time. Because the values are always changing, we need specific ways to measure them.

Peak and Peak-to-Peak Values

  • Peak Value (\(V_0\) or \(I_0\)): The maximum vertical displacement from the zero line. It is the "height" of the wave.
  • Peak-to-Peak Value: The total vertical distance from the very top (crest) to the very bottom (trough). This is simply \(2 \times\) the peak value.

Root Mean Square (rms) Values

If you tried to find the "average" of a sine wave, you would get zero because the positive and negative halves cancel out. However, AC clearly still delivers energy! To compare AC to DC, we use rms values.

The rms value of an alternating current is the value of direct current that would dissipate energy at the same rate in a given resistor. You can think of it as the "effective" value of the AC.

The relationships you need to know are:
\(V_{rms} = \frac{V_0}{\sqrt{2}}\)
\(I_{rms} = \frac{I_0}{\sqrt{2}}\)

Quick Tip: When a question mentions a voltage for a mains supply (like the UK’s \(230\text{ V}\)), it is almost always giving you the rms value, not the peak!

Key Takeaway:

AC power is calculated using rms values: \(P = I_{rms}V_{rms}\) or \(P = I_{rms}^2R\).

2. Using an Oscilloscope

An oscilloscope is essentially a "visual voltmeter." It shows a graph of how voltage varies with time. While you don't need to know how the inside of the machine works, you must know how to read the controls.

The Two Main Controls:

  1. Y-gain (or Y-sensitivity): This tells you how many Volts each major grid square (division) on the vertical axis represents. Measured in \(\text{V/div}\).
  2. Time-base: This tells you how much time each major grid square on the horizontal axis represents. Measured in \(\text{s/div}\), \(\text{ms/div}\), or \(\mu\text{s/div}\).

How to calculate values from the screen:

Step 1: Finding Voltage. Count the number of vertical divisions for the peak height and multiply by the Y-gain.
\(V_0 = \text{number of divisions} \times \text{Y-gain}\)

Step 2: Finding Time Period (\(T\)). Count the horizontal divisions for one full wave cycle and multiply by the Time-base.
\(T = \text{number of divisions} \times \text{Time-base}\)

Step 3: Finding Frequency (\(f\)). Once you have the time period, use the formula:
\(f = \frac{1}{T}\)

3. Transformers

A transformer is a device used to change the amplitude of an alternating voltage. It consists of two coils of wire—the primary and the secondary—wrapped around a laminated soft iron core.

How they work:

1. An alternating current flows through the primary coil.
2. This creates a changing magnetic field in the iron core.
3. The changing magnetic field passes through the secondary coil.
4. According to Faraday’s Law, this "flux linkage" induces an alternating emf in the secondary coil.

The Transformer Equation:

The ratio of the voltages is the same as the ratio of the number of turns in the coils:
\(\frac{N_s}{N_p} = \frac{V_s}{V_p}\)

Where \(N_s\) and \(N_p\) are the number of turns on the secondary and primary coils, and \(V_s\) and \(V_p\) are the voltages.

  • Step-up Transformer: Has more turns on the secondary coil (\(N_s > N_p\)). It increases the voltage.
  • Step-down Transformer: Has fewer turns on the secondary coil (\(N_s < N_p\)). It decreases the voltage.

4. Efficiency and Energy Loss

In an ideal transformer, power in = power out (\(I_p V_p = I_s V_s\)). However, real transformers are never 100% efficient because energy is lost as heat.

Causes of Energy Loss:

  • Eddy Currents: These are tiny loops of induced current in the iron core itself. They cause the core to heat up. To reduce this, the core is laminated (made of thin layers of iron separated by insulators).
  • Resistance in the Coils: The wire has resistance, which generates heat (\(P = I^2R\)). To reduce this, thick copper wire is used.
  • Hysteresis: Energy is required to constantly magnetise and demagnetise the core. Using "soft" iron helps minimize this.

Efficiency Formula:
\(\text{Efficiency} = \frac{I_s V_s}{I_p V_p} \times 100\%\)

5. High-Voltage Transmission (The National Grid)

Why do we use step-up transformers to send electricity at hundreds of thousands of volts across the country? To save energy.

The Logic:

1. Electricity is transmitted through long cables that have a fixed resistance (\(R\)).
2. Power lost as heat in the cables is given by \(P_{loss} = I^2 R\).
3. To reduce \(P_{loss}\), we must reduce the current (\(I\)).
4. Since \(P = IV\), if we want to transmit the same amount of power but with a tiny current, we must use a very high voltage.

Don't worry if this seems backwards! Just remember: High Voltage = Low Current = Low Power Loss.

Key Takeaway:

Step-up transformers are used at power stations to increase voltage (reducing current and heat loss). Step-down transformers are used near homes to decrease voltage to a safe, usable level.

Common Mistakes to Avoid:

  • Confusing Peak and RMS: Always check if the question wants the "peak" or the "rms" value. If you are calculating power, use rms.
  • Units: Oscilloscope time-bases are often in milliseconds (\(10^{-3}\)) or microseconds (\(10^{-6}\)). Don't forget to convert them to seconds before calculating frequency!
  • DC and Transformers: Remember that transformers do not work with DC. If the input current isn't changing, the magnetic field won't change, and no voltage will be induced in the second coil.

Quick Review:

1. \(V_{rms} = \frac{V_0}{\sqrt{2}}\)
2. \(f = \frac{1}{T}\)
3. \(\frac{N_s}{N_p} = \frac{V_s}{V_p}\)
4. Laminating the core reduces eddy currents.
5. High voltage transmission reduces \(I^2R\) power losses.