In a practical loaded transformer operating from an alternating-current (AC) supply, how does the primary current respond when the secondary load current increases, so that mutual induction maintains nearly constant core flux?

Introduction / Context:
Transformers rely on mutual induction: a changing current in the primary creates a changing magnetic flux in the core, which induces voltage in the secondary. When a load is connected, current flows in the secondary and affects the primary via the core. This question tests your understanding of how primary current automatically adjusts to changing secondary load to keep the core flux approximately constant in steady operation.

Given Data / Assumptions:

• Ideal transformer approximation (small losses).
• Constant AC primary voltage.
• Magnetizing current is comparatively small.
• Secondary load current increases due to added load.

Concept / Approach:
The secondary load current produces a demagnetizing magnetomotive force (MMF) that tends to reduce core flux. To counteract this and maintain the flux set by the applied primary voltage, the primary current increases. The additional component of primary current (the load component) creates an opposing MMF that balances the secondary's effect, keeping net flux nearly unchanged.

Step-by-Step Solution:
Primary applied voltage fixes core flux waveform approximately (neglecting saturation).Secondary load current introduces a demagnetizing MMF: N2 * I2.Transformer action draws extra primary current I1(load) so that N1 * I1(load) ≈ N2 * I2 (ampere-turns balance).Total primary current = magnetizing current + load component; thus it increases with secondary load.

Verification / Alternative check:
Using power balance for an ideal transformer: V1 * I1 ≈ V2 * I2. If I2 increases at fixed V2, then I1 must increase at fixed V1, confirming the qualitative behavior.

Why Other Options Are Wrong:

• Primary decrease when secondary increases: Opposite of ampere-turns balance.
• Primary remains fixed: Violates power and MMF balance.
• “Secondary decrease causes primary increase”: Also contrary to balance; less load means less primary current.

Common Pitfalls:

• Confusing magnetizing current (relatively small) with total primary current.
• Forgetting that the applied voltage, not the load, primarily sets the flux; current adjusts to maintain it.

Final Answer:
primary current is increased by an increase in secondary current