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Question #43157

Difficulty: 8/10 | 🟢 Free

The Question

A non-ideal transformer has a primary-to-secondary turns ratio of $1:n$ . The primary winding has a finite magnetizing inductance $L_m$ (in H) and negligible resistance. The secondary winding is connected to a series load consisting of a resistor $R$ (in $\Omega$ ), an inductor $L$ (in H), and a capacitor $C$ (in F). An AC voltage source of frequency $\omega$ (in rad/s) is applied to the primary. It is observed that the total primary current is exactly in phase with the applied primary voltage. Which of the following conditions must necessarily hold true at this frequency?

Options

A.
$n^2 \omega L_m \ge 2R$
B.
$n^2 \omega L_m \le 2R$
C.
$\omega L_m \ge 2n^2 R$
D.
$\omega L_m \le 2n^2 R$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Frequency Sensitivity of Z|Transformer Flux Linkage

Why This Question Is Tricky

Common Mistakes

Students typically treat transformers as ideal devices, incorrectly assuming that unity power factor in the primary occurs exactly at the secondary's LCR resonance ( $\omega = 1/\sqrt{LC}$ ).

This question traps students who ignore the magnetizing current required to establish the core flux.

By modeling the non-ideal transformer with a parallel magnetizing inductance, students must use complex phasor analysis to find the true resonance condition.

The trap exposes the misconception that flux linkage and primary current are independent of the load's reactive power profile.

It demonstrates that the secondary must actually be capacitive to cancel the primary's inductive magnetizing current, and that a minimum magnetizing reactance is required for this cancellation to even be mathematically possible.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Alternating Current - Class 12
Concept	Frequency Sensitivity of Z
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free