5.4.6 Transformers

Most of us encounter electrical transformers daily. The electronic device you are using right now connects to a mains supply delivering 120 V or 240 V AC, yet its internal microcircuits require a much lower voltage (such as 5 V or 12 V DC) to operate safely and efficiently. A transformer performs this critical task by stepping down or stepping up AC voltage levels.

The Physics of Mutual Induction

In essence, a transformer operates on the principles of Faraday's Law of Induction and conservation of energy through a process called mutual induction:

• Primary Circuit: An alternating current (AC) in the primary coil generates a continuously changing magnetic flux (ΔΦ⁄Δt).
• Iron Core: A soft iron core channels and concentrates this changing flux directly through to the secondary coil with minimal flux leakage.
• Secondary Circuit: As this changing magnetic flux cuts through the secondary coil, it induces an alternating electromotive force (EMF) across its terminals.

The Transformer Equations

The ratio of secondary voltage (V_s) to primary voltage (V_p) is strictly governed by the turns ratio of the two coils:

Assuming an ideal transformer (100% power efficiency where P_in = P_out, or V_pI_p = V_sI_s):

• Step-Up Transformer (N_s > N_p): Increases voltage (V_s > V_p) while proportionally decreasing current (I_s < I_p).
• Step-Down Transformer (N_s < N_p): Decreases voltage (V_s < V_p) while proportionally increasing current (I_s > I_p).

Watch the videos below to explore these mathematical models, examine how real-world transformers minimize energy losses (such as eddy current heating in laminated cores), and work through sample calculations.

Specialized Application: The Induction Coil

Standard transformers rely on an alternating current (AC) supply to generate a continuously changing magnetic flux. However, an induction coil (or Ruhmkorff coil) is a specialized electrical step-up transformer designed to generate extremely high-voltage electrical pulses from a low-voltage direct current (DC) power source, such as a battery.

How an Induction Coil Works

Because a steady DC source produces a constant magnetic field (ΔΦ⁄Δt = 0), an induction coil uses an automatic mechanical switch (an interrupter or contact breaker) to rapidly make and break the primary circuit:

• Rapid Flux Collapse: When the interrupter opens, the magnetic field in the soft iron core collapses almost instantaneously. This produces an extremely large rate of change of flux (^ΔΦ⁄_Δt) over a very short time interval (Δt).
• High Voltage Step-Up: According to Faraday's Law (ε = -N · ^ΔΦ⁄_Δt), this rapid field collapse—combined with a secondary winding containing tens of thousands of turns (N_s >> N_p)—induces high-voltage output pulses across the secondary terminals, often reaching tens of thousands of Volts.
• Role of the Capacitor: A capacitor connected across the interrupter contacts absorbs back-EMF energy to prevent sparking across the breaker points, causing an even sharper collapse of the primary magnetic field.

Watch the short video below to see a physical induction coil in action and examine how its interrupter mechanism produces high-voltage sparks.