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Question #43078

Difficulty: 8/10 | 🟢 Free

The Question

A real transformer is modeled as an ideal transformer with a primary-to-secondary turns ratio of $N_1 : N_2 = 1 : 2$ , in series with a secondary leakage inductance $L_l = 20 \text{ mH}$ . The primary winding is driven by an AC voltage source $V_1(t) = 100 \sin(\omega t) \text{ V}$ . The secondary terminals of the transformer are connected to a load consisting of a resistor $R = 50 \ \Omega$ and a capacitor $C = 50 \ \mu\text{F}$ in series. The angular frequency $\omega$ of the source is adjusted such that the secondary current $I_2(t)$ is exactly $180^\circ$ out of phase with the primary voltage $V_1(t)$ . Calculate the peak voltage across the secondary terminals of the transformer at this frequency.

Options

A.
$40\sqrt{29} \text{ V}$
B.
$200 \text{ V}$
C.
$120 \text{ V}$
D.
$280 \text{ V}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Transformer Flux Linkage|Frequency Sensitivity of Z|Bandwidth in RLC

Why This Question Is Tricky

Common Mistakes

This question tests the transition from an ideal transformer model to a real-world AC circuit model.

Students commonly fall into the trap of assuming $V_{terminal} = (N_2/N_1)V_1 = 200 \text{ V}$ (Option B), ignoring the internal voltage drop across the leakage inductance.

Furthermore, even if they identify the resonance condition required for the $180^\circ$ phase shift, they often mistakenly assume that because the reactive components 'cancel out' for the total circuit, the terminal voltage is simply the voltage across the resistor.

They fail to recognize that the leakage inductance is internal to the transformer, meaning the accessible terminal voltage is the phasor sum of the resistive and capacitive voltage drops, which actually exceeds the ideal induced EMF due to the capacitive nature of the load.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Alternating Current - Class 12
Concept	Transformer Flux Linkage
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free