How does a change in primary resistance affect an ideal transformer?

How Does the Change in Primary Resistance Affect an Ideal Transformer?

The change in primary resistance has significant implications for the performance of an ideal transformer, especially in practical applications. While an ideal transformer assumes no losses, real-world transformers have some resistance in both the primary and secondary windings, which can affect performance. Below is a detailed explanation of how changes in primary resistance impact an ideal transformer:

Assumptions of an Ideal Transformer

• Zero Resistance: An ideal transformer assumes that the resistance of both the primary and secondary windings is zero.

• No Core Losses: An ideal transformer assumes no hysteresis or eddy current losses in the core.

• Perfect Coupling: An ideal transformer assumes perfect magnetic coupling between the primary and secondary windings, with no leakage flux.

Impact of Primary Resistance

Voltage Drop:

In a real transformer, the resistance Rp of the primary winding causes a voltage drop. As the load current increases, the primary current Ip also increases, and according to Ohm's law V=I⋅R, the voltage drop across the primary winding Vdrop =Ip ⋅Rp increases.

This voltage drop reduces the primary voltage Vp , which in turn affects the secondary voltage Vs . The secondary voltage is calculated using the formula:

where Ns and Np are the number of turns in the secondary and primary windings, respectively. If Vp decreases due to the resistance, Vs will also decrease.

Reduced Efficiency:

The presence of primary resistance leads to copper losses, which are resistive losses. Copper losses can be calculated using the formula Ploss=Ip2⋅Rp.

These losses increase the total losses in the transformer, reducing its efficiency. Efficiency η can be calculated using the formula:

where 

Pout is the output power and 

Pin is the input power.

Temperature Rise:

• Copper losses cause the primary winding to heat up, leading to a temperature rise. This temperature rise can affect the insulation material, reducing the transformer's lifespan and reliability.

• The temperature rise can also cause thermal stress on other components, such as the core and insulation materials, further impacting performance.

Load Characteristics:

• Changes in primary resistance affect the load characteristics of the transformer. When the load changes, variations in primary current and voltage can cause changes in the secondary voltage, affecting the load's operating state.

• For applications requiring a constant output voltage, changes in primary resistance can lead to unstable output voltage, impacting the proper operation of connected devices.

Conclusion

While an ideal transformer assumes zero resistance, in practical applications, changes in primary resistance significantly affect the performance of a transformer. Primary resistance can cause voltage drops, reduce efficiency, increase temperature, and alter load characteristics. Understanding these impacts is crucial for designing and using transformers effectively. Measures such as selecting low-resistance wire, implementing cooling solutions, and optimizing load management can help improve transformer performance and reliability.