Recall and use the equation V_p / V_s = N_p / N_s where p and s refer to primary and secondary

4.5.6 The Transformer ⚡️

What is a transformer?

A transformer is a device that changes the voltage of an alternating current (AC) without changing its frequency. Think of it like a pair of gear wheels – if you turn one wheel (the primary) faster or slower, the other wheel (the secondary) will turn at a different speed, giving you a different voltage.

Key Equation

The relationship between the voltages and the number of turns on the coils is given by:

$$\frac{V_p}{V_s} = \frac{N_p}{N_s}$$

Where:

• $V_p$ = primary voltage (input)
• $V_s$ = secondary voltage (output)
• $N_p$ = number of turns on the primary coil
• $N_s$ = number of turns on the secondary coil

Why does it work?

When the primary coil carries an AC current, it creates a changing magnetic field. This changing field induces a voltage in the secondary coil. The amount of voltage induced depends on how many times the magnetic field cuts across the secondary turns – that’s why the number of turns matters.

Practical Example

1. Suppose a transformer has $N_p = 200$ turns and $N_s = 800$ turns.
2. If the primary voltage is $V_p = 120\,\text{V}$, what is the secondary voltage?
3. Using the equation:

$$\frac{V_p}{V_s} = \frac{N_p}{N_s} \;\;\Rightarrow\;\; V_s = V_p \times \frac{N_s}{N_p}$$

4. Plug in the numbers:

$$V_s = 120\,\text{V} \times \frac{800}{200} = 120\,\text{V} \times 4 = 480\,\text{V}$$

5. So the transformer steps up the voltage from 120 V to 480 V.

Transformer Types

• Step‑up – increases voltage (more turns on secondary).
• Step‑down – decreases voltage (fewer turns on secondary).
• Isolation – provides electrical isolation while keeping voltage roughly the same.

Quick Check

Answer the following questions to test your understanding:

1. If a transformer has a primary voltage of 240 V and 500 turns on the primary, how many turns should the secondary have to produce 120 V?
2. What happens to the secondary voltage if you double the number of turns on the secondary while keeping the primary voltage constant?

Table: Common Transformer Ratios