Question

A step-down transformer has 4000 turns on the primary and 200 turns on the secondary. If the primary voltage amplitude is \(2.2 \mathrm{kV},\) what is the secondary voltage amplitude?

Short answer

Answer: The secondary voltage amplitude is 0.11 kV or 110 V.

Step-by-step solution

Identify the given information

In this exercise, we are given the following information: - Primary coil turns (N1) = 4000 turns - Secondary coil turns (N2) = 200 turns - Primary voltage amplitude (V1) = 2.2 kV Our goal is to find the secondary voltage amplitude (V2).

Find the turns ratio

The turns ratio is the ratio between the number of turns in the primary coil to the number of turns in the secondary coil: Turns Ratio, \(k = \frac{N1}{N2}\) Plug the given values of N1 and N2 into the formula: \(k = \frac{4000}{200} = 20\)

Calculate the secondary voltage amplitude

Now that we have the turns ratio, we can calculate the secondary voltage amplitude V2. For transformers, the voltage ratio is equal to the turns ratio: \(k = \frac{V1}{V2}\) Rearrange the formula to find V2: \(V2 = \frac{V1}{k}\) Plug in the given primary voltage amplitude (V1 = 2.2 kV) and the turns ratio (k = 20) into the formula: \(V2 = \frac{2.2\, \text{kV}}{20}\) Calculate the secondary voltage amplitude: \(V2 = 0.11\, \text{kV}\) or \(110\, \text{V}\)

Write the final answer

The secondary voltage amplitude of the step-down transformer is 0.11 kV or 110 V.