# Transformer Testing: Calculating Series Inductance and Input Voltage

## What are the given parameters for calculating series inductance and input voltage in a transformer testing scenario?

A 120 KVA transformer with a resistance and reactance of 1% and 5% respectively is used to test a cable at 400 kV at 50 Hz. The cable takes a charging current of 0.5 A at 400 kV. What is the series inductance required and the input voltage to the transformer?

## Series Inductance and Input Voltage Calculation:

The series inductance required is approximately 127.32 H. The input voltage to the transformer is approximately 0.0255 V.

To determine the series inductance required and the input voltage to the transformer, we can use the given information and the formulas for reactance and impedance.

First, let's calculate the series inductance required: Given: Transformer power (KVA): 120 KVA Transformer voltage (V): 250 V/200 KV Transformer resistance: 1% Transformer reactance: 5% Cable voltage (V): 400 kV Cable charging current (A): 0.5 A Frequency (Hz): 50 Hz

Using the formula for inductance, L = X / (2 * π * f), we can calculate the series inductance required: L = (5% * 400 kV) / (2 * π * 50 Hz) L = (0.05 * 400,000 V) / (2 * 3.14159 * 50 Hz) L ≈ 127.32 H

Therefore, the series inductance required is approximately 127.32 H.

Next, let's determine the input voltage to the transformer: Using the formula for impedance, Z = √(R^2 + X^2), we can calculate the impedance: Z = √((1%^2) + (5%^2)) Z = √(0.01^2 + 0.05^2) Z ≈ 0.051 H

Now, we can calculate the input voltage: V = I * Z V = 0.5 A * 0.051 H V ≈ 0.0255 V

Therefore, the input voltage to the transformer is approximately 0.0255 V.