Transformer Calculations

Transformers change the size of an a.c. voltage. Think of them like bicycle gears: one gear trades speed for force. A transformer trades voltage for current using two coils of wire around a soft iron core.

Key quantities

• Primary (p): the input coil (voltage in).
• Secondary (s): the output coil (voltage out).
• N: number of turns (no unit). V: voltage (V). I: current (A).

Core formulas (ideal, 100% efficient)

Voltage is proportional to turns:

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

For 100% efficiency, input power = output power:

$$V_p I_p = V_s I_s$$

So current changes in the opposite ratio to voltage/turns:

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

Step-up vs step-down

• Step-up: $N_s > N_p$ so $V_s > V_p$ and $I_s < I_p$.
• Step-down: $N_s < N_p$ so $V_s < V_p$ and $I_s > I_p$.

Common mistakes

• Mixing up p and s. Always label clearly.
• Forgetting units: V for voltage, A for current, turns have no unit.
• Thinking power increases. In ideal transformers, $P_{in}=P_{out}$; real ones have small losses.
• Using these formulas with d.c. Transformers work with a.c.

Real-world link: Power lines use step-up transformers to raise voltage and reduce current, lowering heating losses in cables.