Problems solved about Ideal Transformer

Problem 91-9 Source: Problem developed by the site author.

A coil with 400 turns is completely traversed by a magnetic flux given by Φ = 4 sen 377 t + 0.05 sen 1,131 t (mWb). Find:

a) the instantaneous voltage induced in the coil.

b) the effective (or RMS) voltage induced in the coil.

Solution of the Problem 91-9

Item a

To solve this item we will use eq. 91-06 repeated below.

eq. 91-06

Replacing the variables by their respective numerical values and deriving the function Φ, we obtain:

E = 400 ( 377 x 4 sen 377 t + 1,131 x 0.05 sen 1,131 t)

Performing the calculation, we obtain:

E = 603.2 sen 377 t + 22.62 sen 1,131 t V

Item b

Since the induced voltage has the third harmonic, then to calculate the effective voltage we must use eq. 91-14 shown below.

eq. 91-14

Replacing the variables with their respective numerical values, we have:

_ef

Performing the calculation, we obtain:

_ef

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