A 5 kVA, 50 V/100 V, single-phase transformer has a secondary terminal voltage of 95 V when loaded. The regulation of the transformer is

Understanding Transformer Voltage Regulation

Transformer voltage regulation measures how well the transformer maintains its secondary voltage under varying load conditions. Specifically, it quantifies the voltage drop from the no-load condition to the full-load condition, expressed as a percentage of the full-load voltage.

Calculating Transformer Voltage Regulation

The formula for calculating voltage regulation (VR) is:

$$\text{VR}=\frac{V_{\text{NL}}-V_{\text{FL}}}{V_{\text{FL}}}\times 100\%$$

Where:

- $V_{\text{NL}}$ is the no-load secondary terminal voltage.
- $V_{\text{FL}}$ is the full-load secondary terminal voltage.

Analyzing the Given Transformer Data

From the question, we have the following information:

- Transformer Rating: 5 kVA
- Primary Voltage: 50 V
- Secondary Voltage (No Load, $V_{\text{NL}}$): 100 V
- Secondary Terminal Voltage (Loaded, $V_{\text{FL}}$): 95 V

Step-by-Step Voltage Regulation Calculation

1. Identify the no-load secondary voltage ($V_{\text{NL}}$). In this case, it's the rated secondary voltage, which is 100 V.
2. Identify the full-load secondary voltage ($V_{\text{FL}}$). This is the voltage when the transformer is loaded, given as 95 V.
3. Substitute these values into the voltage regulation formula:

$$\text{VR}=\frac{100\text{ V}-95\text{ V}}{95\text{ V}}\times 100\%$$

$$\text{VR}=\frac{5\text{ V}}{95\text{ V}}\times 100\%$$

$$\text{VR}\approx 0.05263\times 100\%$$

$$\text{VR}\approx 5.26\%$$

Comparing Calculation with Options

The calculated voltage regulation is approximately 5.26%. Let's compare this with the given options:

- 4.5%
- 9%
- 5%
- 1%

The calculated value of 5.26% is closest to the option 5%. Therefore, the regulation of the transformer is approximately 5% under the specified load condition.