The question asks about the efficiency of a power transformer when operating under a matched load condition. To understand this, we must first consider what constitutes an ideal transformer and how its efficiency is defined.

Transformer Efficiency Fundamentals

Efficiency of any electrical device, including a power transformer, is defined as the ratio of output power to input power. It indicates how effectively the device converts input electrical power into useful output electrical power.

The formula for transformer efficiency ($\eta$) is given by:

$$\eta = \frac{\text{Output Power}}{\text{Input Power}} \times 100\%$$

Alternatively, since Input Power = Output Power + Losses, the efficiency can also be expressed as:

$$\eta = \frac{\text{Output Power}}{\text{Output Power} + \text{Losses}} \times 100\%$$

Or,

$$\eta = \frac{\text{Input Power} - \text{Losses}}{\text{Input Power}} \times 100\%$$

Transformer Losses

In a practical power transformer, there are typically two main types of losses that prevent it from achieving 100% efficiency:

• Core Losses (Iron Losses): These losses occur in the transformer's magnetic core due to alternating magnetic flux. They include hysteresis loss (energy dissipated during magnetization cycles) and eddy current loss (losses from circulating currents induced in the core).
• Copper Losses ($I^2R$ Losses): These losses occur in the windings (copper coils) of the transformer due to the resistance of the wire. As current flows through the windings, heat is generated ($I^2R$), leading to power loss. These losses are load-dependent, increasing with the square of the load current.

Ideal Transformer Concept

An ideal transformer is a theoretical concept used for simplified analysis. An ideal transformer is assumed to have the following characteristics:

• No winding resistance, therefore zero copper losses.
• No magnetic leakage flux.
• Core has infinite permeability, requiring negligible magnetizing current.
• No core losses (zero hysteresis and eddy current losses).

In an ideal transformer, there are no losses, meaning all the input power is perfectly transferred to the output. Therefore, for an ideal transformer:

$$\text{Input Power} = \text{Output Power}$$

Matched Load Condition and Efficiency

The term "matched load condition" for a power transformer, especially when 100% efficiency is an option, implies an ideal scenario. In this context, it suggests a perfect transfer of power without any dissipation or loss within the transformer itself. If the load is perfectly "matched" and the transformer operates without any internal losses, then 100% of the input power would be delivered to the load.

For a practical power transformer, maximum efficiency typically occurs when the variable copper losses are equal to the constant core losses. However, even at maximum efficiency, a real transformer's efficiency is always less than 100% because losses (both core and copper) are always present.

Since the question presents 100% as a possible answer for the efficiency of a power transformer under matched load condition, it refers to the theoretical ideal case where the transformer is assumed to be loss-free and perfectly efficient in power transfer to a load that allows for maximum (ideal) power delivery.

Why 100% Efficiency for Power Transformer

Given the options, the mention of "matched load condition" leading to 100% efficiency implies that we are considering an ideal power transformer. In an ideal transformer, there are no losses (no core losses, no copper losses). Consequently, the input power exactly equals the output power, leading to 100% efficiency. This is a theoretical upper limit for efficiency.

Therefore, for an ideal power transformer operating under a condition where it can perfectly transfer power (interpreted as "matched load condition" in this context), its efficiency is 100%.