The flux involved in the emf equation of a transformer has

Question

Examoogle · Accepted Answer

maximum value

Explanation: The EMF equation of a transformer is derived from Faraday's law of electromagnetic induction, which relates the induced EMF to the rate of change of flux. In this derivation, the flux is assumed to be sinusoidal ($\Phi = \Phi_m \sin(\omega t)$), and the induced EMF is proportional to the peak value of the flux, denoted as $\Phi_m$.

Working Principle: When an alternating voltage is applied to the primary winding, it produces a sinusoidally varying magnetic flux in the core. The induced EMF is given by $e = -N \frac{d\Phi}{dt}$. By substituting $\Phi = \Phi_m \sin(\omega t)$, the EMF becomes $e = -N \Phi_m \omega \cos(\omega t)$. The peak (maximum) value of this EMF is $E_m = N \Phi_m \omega$, where $\Phi_m$ is the maximum flux.

Key Formulas: $E_1 = 4.44 f N_1 \Phi_m$ — RMS induced EMF in primary winding; $E_2 = 4.44 f N_2 \Phi_m$ — RMS induced EMF in secondary winding

Key Points: The transformer flux is assumed to be purely sinusoidal.; The constant 4.44 arises from $\sqrt{2} \times \pi \approx 4.44$.; $\Phi_m$ represents the peak value of the magnetic flux in the core.

Advantages: Simplifies transformer design calculations.; Allows direct derivation of turns ratio based on voltage ratings.

Disadvantages: Assumes an ideal sinusoidal flux which may be distorted by core saturation.; Neglects leakage flux which does not link both windings.

Applications: Transformer winding design.; Core area estimation.; Determining flux density limits.

Additional Info: The term 4.44 is derived as $4.44 = 4 \times 1.11 \times 1.0$, where 1.11 is the form factor of a sine wave.. Option A (rms) is incorrect because the EMF depends on the peak variation of flux rather than its RMS value. Option B (average) is also incorrect as it doesn't represent the peak magnitude required for the induced peak voltage.

Answer: D is correct — The emf equation $E = 4.44 f N \Phi_m$ uses the maximum value of flux $\Phi_m$ to determine the peak-to-peak change in magnetic linkage.

Exam Tip: Always remember that 4.44 is $4 \times \text{Form Factor} \times \text{Frequency}$. If the flux were not sinusoidal, the constant would change based on the waveform's form factor.

Related Questions

Discussion (0)