Transformer Action

Introduction to Transformers

• A transformer is a device that transfers electrical energy from one circuit to another through electromagnetic induction.
• Transformers are crucial for efficient electricity transmission over long distances by stepping up voltage and stepping down voltage for safe use in homes and businesses.
• Transformers operate on the principle of electromagnetic induction, where a changing magnetic flux induces an electromotive force (EMF).

KEY TAKEAWAY: Transformers rely on electromagnetic induction to efficiently transfer electrical energy between circuits.

Ideal Transformer

• An ideal transformer is a theoretical model of a transformer that assumes 100% efficiency and no energy losses.
• In reality, transformers do experience small energy losses due to factors such as resistance in the coils and hysteresis in the core, but for VCE Physics calculations, transformers can be treated as ideal unless otherwise stated.

Transformer Components

• Primary Coil: The coil connected to the input voltage source. Designated with subscript ‘p’.
• Secondary Coil: The coil connected to the load. Designated with subscript ‘s’.
• Core: A ferromagnetic core that links the two coils and enhances the magnetic flux.

Transformer Operation

1. Alternating Current (AC) Input: An alternating current in the primary coil creates a changing magnetic flux in the core.
2. Magnetic Flux Linkage: The changing magnetic flux links the secondary coil.
3. Induced EMF: According to Faraday’s Law of Electromagnetic Induction, the changing magnetic flux induces an electromotive force (EMF) in the secondary coil.
4. Voltage Transformation: The ratio of the number of turns in the primary and secondary coils determines the voltage transformation.

STUDY HINT: Visualizing the changing magnetic field lines linking both coils can help understand transformer operation.

Transformer Equations

Turns Ratio and Voltage Ratio

• The ratio of the number of turns in the primary coil ($N_p$) to the number of turns in the secondary coil ($N_s$) is called the turns ratio.

• For an ideal transformer, the voltage ratio is equal to the turns ratio:

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

  Where:

  • $V_s$ = Voltage in the secondary coil
  • $V_p$ = Voltage in the primary coil
  • $N_s$ = Number of turns in the secondary coil
  • $N_p$ = Number of turns in the primary coil

Power Conservation

• In an ideal transformer, power is conserved. Therefore, the power in the primary coil ($P_p$) is equal to the power in the secondary coil ($P_s$):

  $$P_p = P_s$$

  $$I_p V_p = I_s V_s$$

  Where:

  • $I_p$ = Current in the primary coil
  • $V_p$ = Voltage in the primary coil
  • $I_s$ = Current in the secondary coil
  • $V_s$ = Voltage in the secondary coil

Current Ratio

• From the power conservation equation, we can derive the relationship between the current ratio and the turns/voltage ratio:

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

Summary Equation

• Combining all the ratios, we get the key equation for ideal transformers:

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

REMEMBER: The voltage and number of turns are directly proportional, while the current is inversely proportional.

Step-Up and Step-Down Transformers

• Step-Up Transformer: A transformer that increases the voltage from the primary to the secondary coil. This occurs when $N_s > N_p$ and $V_s > V_p$.

• Step-Down Transformer: A transformer that decreases the voltage from the primary to the secondary coil. This occurs when $N_s < N_p$ and $V_s < V_p$.

VCAA FOCUS: VCAA often presents problems involving calculating voltage, current, or number of turns in step-up and step-down transformers.

Applications of Transformers

• Power Transmission: Step-up transformers increase voltage for efficient long-distance transmission, reducing current and minimizing power loss due to resistance in transmission lines ($P_{loss} = I^2R$). Step-down transformers then reduce the voltage to safe levels for residential and industrial use.
• Electronic Devices: Transformers are used in power adapters to convert high voltage AC from the mains to lower voltage DC required by electronic devices.
• Electrical Isolation: Transformers can provide electrical isolation between circuits, enhancing safety.

APPLICATION: High-voltage transmission lines use step-up transformers to minimize power loss during electricity transmission.

Example Problem

A transformer has 500 turns in its primary coil and 100 turns in its secondary coil. If the primary voltage is 240 V AC, what is the secondary voltage? If the primary current is 0.5 A, what is the secondary current, assuming an ideal transformer?

Solution:

1. Voltage Calculation:

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

   $$V_s = V_p \times \frac{N_s}{N_p} = 240 \text{ V} \times \frac{100}{500} = 48 \text{ V}$$

2. Current Calculation:

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

   $$I_s = I_p \times \frac{N_p}{N_s} = 0.5 \text{ A} \times \frac{500}{100} = 2.5 \text{ A}$$

EXAM TIP: Always clearly identify the primary and secondary values before applying the transformer equations.

Limitations of the Ideal Transformer Model

• Real transformers are not 100% efficient. They experience energy losses due to:
  • Hysteresis Loss: Energy lost due to the repeated magnetization and demagnetization of the core.
  • Eddy Current Loss: Energy lost due to induced currents in the core material.
  • Copper Loss: Energy lost due to the resistance of the coil windings ($I^2R$ loss).
  • Flux Leakage: Not all the magnetic flux produced by the primary coil links the secondary coil.

COMMON MISTAKE: Forgetting that real transformers have losses and assuming 100% efficiency in all situations. However, in VCE physics, unless specified, assume the transformer is ideal.