Question: Which of the following quantity/quantities remains same in primary and secondary coils of an ideal transformer?
Step 1 (Governing Principle): [0.5 Mark]
An ideal transformer is defined by two fundamental physical conditions:
- Perfect Flux Linkage: The core is assumed to have infinite permeability, ensuring that the magnetic flux $\phi$ produced by the primary coil is entirely linked with the secondary coil without any leakage. Thus, $\phi_p = \phi_s$.
- Conservation of Energy: For an ideal transformer, there are no energy losses (i.e., no hysteresis, eddy current, or copper losses). Therefore, the input power ($P_{in}$) must equal the output power ($P_{out}$).
Step 2 (Mathematical Working): [0.25 Mark]
Based on the principle of conservation of energy for an ideal transformer:
$$P_{in} = P_{out}$$ $$V_p I_p = V_s I_s$$Where $V$ represents voltage and $I$ represents current. Since $V_p \neq V_s$ (unless it is a 1:1 transformer) and $I_p \neq I_s$ (due to the transformer ratio), only the product $VI$ (Power) remains constant. Additionally, by Faraday's Law of Induction, the rate of change of flux is the same for both coils:
$$\frac{d\phi_p}{dt} = \frac{d\phi_s}{dt}$$Step 3 (Final Concluded Answer): [0.25 Mark]
Since both the magnetic flux (linked through the core) and the power (due to no energy loss) remain the same in an ideal transformer, the correct option is (D).
Correct Option: (D) Magnetic flux and Power both
💡 EL10 Concept Insight: Imagine the transformer as a perfect energy pipe; because it's "ideal," no energy leaks out, so the power going in is exactly what comes out. Also, because the iron core acts like a perfect bridge for magnetism, the magnetic "message" sent by the first coil is received perfectly by the second coil without losing any strength.