If R is the resistance of a secondary winding of a transformer and K is the transformation ratio, then the equivalent secondary resistance referred to primary will be
Understand the Problem
The question is asking for the equivalent secondary resistance referred to the primary for a transformer based on the given resistance of the secondary winding and the transformation ratio.
Answer
The equivalent secondary resistance referred to the primary will be $R \times K^2$.
Answer for screen readers
The equivalent secondary resistance referred to the primary will be $R \times K^2$.
Steps to Solve
- Understand the transformer equation
For a transformer, the equivalent resistance referred to the primary side can be calculated using the formula $R_{eq} = R \times K^2$, where $R$ is the secondary resistance and $K$ is the transformation ratio.
- Identify the variables
In this case,
- Let $R$ be the resistance of the secondary winding,
- Let $K$ be the transformation ratio.
- Substitute into the equation
We substitute the known values into the equation for equivalent resistance: $$R_{eq} = R \times K^2$$
This means the equivalent resistance referred to the primary will be affected by the square of the transformation ratio.
The equivalent secondary resistance referred to the primary will be $R \times K^2$.
More Information
In transformers, the transformation ratio ($K$) relates the primary and secondary voltages, and its square affects the impedance and resistance when referred between sides. This principle is crucial for proper transformer design and its applications.
Tips
- Confusing the transformation ratio $K$ with other ratios (like turns ratio); remember that $K$ is derived from turns ratio but relates specifically to voltage.
- Forgetting to square the transformation ratio when calculating the equivalent resistance.
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