Answer to Question #102354 in Electric Circuits for samsuddin

Question

Given the input current 15A and the output voltage of 100V for a step-up transformer
having 90% efficiency, find the output power and the voltage in the secondary if the
output current is 3 A.

Answer 1

a) By the definition of the efficiency we have:

$$\eta = \dfrac{P_{output}}{P_{input}} \cdot 100 \%,$$

here, $P_{input}$ is the input power in the primary (input) winding of the transformer, $P_{output}$ is the output power in the secondary (output) winding of the transformer, $\eta = 90 \%$ is the efficiency of the transformer.

We can find the input power from the formula:

$$P_{input} = I_{input}V_{input},$$

here, $I_{input} = 15A$ is the input current in the primary winding of the transformer and $V_{input} = 100V$ is the input voltage in the primary winding of the transformer.

Substituting the expression for $P_{input}$ into the formula for the efficiency we can calculate the output power in the secondary winding of the transformer:

$$P_{output} = \dfrac{\eta}{100 \%} I_{input}V_{input} = \dfrac{90 \%}{100 \%} \cdot 15A \cdot 100V = 1350W.$$

b) We can find the output voltage in the secondary winding of the transformer from the formula:

$$P_{output} = I_{output}V_{output},$$ $$V_{output} = \dfrac{P_{output}}{I_{output}} = \dfrac{1350W}{3A} = 450V.$$

Answer:

a) $P_{output} = 1350W.$

b) $V_{output} = 450V.$