Question

31.6 transformers

in an ideal 1:8 step - up transformer, the primary power is 10.0 kw and the secondary current is 25 a. the primary voltage is

50 v.
6.3 v.
400 v.
3200 v.
26000 v.

Explanation:

Step1: Calculate secondary voltage

For an ideal transformer, \(P_{primary}=P_{secondary}\). Given \(P = 10000\space W\) and \(I_{secondary}=25\space A\). Using \(P = V\times I\), we can find \(V_{secondary}=\frac{P}{I_{secondary}}\).

$$V_{secondary}=\frac{10000}{25}=400\space V$$

Step2: Use transformer turns - voltage ratio

For a transformer, \(\frac{V_{primary}}{V_{secondary}}=\frac{N_{primary}}{N_{secondary}}\). Given \(\frac{N_{primary}}{N_{secondary}}=\frac{1}{8}\), then \(V_{primary}=\frac{V_{secondary}}{8}\)

$$V_{primary}=\frac{400}{8}=50\space V$$

Answer:

50 V.