Transformers and Mutual Inductance Reference Cheat Sheet

Key Facts

• For an ideal transformer, the voltage ratio equals the turns ratio: $\frac{V_s}{V_p} = \frac{N_s}{N_p}$.
• For an ideal transformer, the current ratio is inverse to the turns ratio: $\frac{I_s}{I_p} = \frac{N_p}{N_s}$.
• Ideal transformer power is conserved, so $P_p = P_s$ and $V_p I_p = V_s I_s$.
• A step-up transformer has $N_s > N_p$ and increases voltage according to $V_s > V_p$.
• A step-down transformer has $N_s < N_p$ and decreases voltage according to $V_s < V_p$.
• Mutual inductance relates induced emf in one coil to changing current in another: $\mathcal{E}_2 = -M\frac{dI_1}{dt}$.
• For a coil, self-induced emf is given by $\mathcal{E} = -L\frac{dI}{dt}$.
• Transformer efficiency is $\eta = \frac{P_{out}}{P_{in}} \times 100\%$.

Vocabulary

Transformer

A device that uses electromagnetic induction between coils to change alternating voltage and current levels.

Primary Coil

The coil connected to the input voltage source in a transformer.

Secondary Coil

The coil connected to the output circuit where an induced voltage appears.

Turns Ratio

The ratio of secondary turns to primary turns, written as $\frac{N_s}{N_p}$, which determines the ideal voltage ratio.

Mutual Inductance

A measure of how effectively a changing current in one coil induces an emf in another coil.

Induced emf

A voltage produced by a changing magnetic flux, often described by Faraday’s law.