The co-efficient of coupling between two air core coils depends on

Question

Examoogle · Accepted Answer

Option C: Mutual inductance and self inductance of two coils

Explanation & Concepts:
The coefficient of coupling ($k$) is a dimensionless parameter that represents the degree of magnetic coupling between two inductive coils. It defines the ratio of mutual inductance to the square root of the product of individual self-inductances.

Working Principle: In air-core coils, the coupling depends on the geometry, orientation, and proximity of the coils. Since $M = k \sqrt{L_1 L_2}$, the coefficient is mathematically derived from both the mutual inductance ($M$) and the self-inductances ($L_1, L_2$) of the respective coils, signifying what fraction of the magnetic flux produced by one coil links with the other.

Key Formulas: $k = \frac{M}{\sqrt{L_1 L_2}}$ — Fundamental definition of coupling coefficient; $M = k\sqrt{L_1 L_2}$ — Practical expression for mutual inductance

Key Points: The value of $k$ ranges from $0$ to $1$.; For air-core coils, $k$ is usually very small due to flux leakage.; $k=1$ represents perfectly coupled coils (ideal transformer scenario).; $k=0$ indicates magnetically isolated coils.

Advantages: Allows quantitative analysis of energy transfer efficiency; Helps in designing high-frequency transformers and resonant circuits

Disadvantages: Does not account for non-linear saturation effects in ferromagnetic cores; Assumes constant inductance values under all conditions

Applications: RF tuning circuits; Wireless power transfer systems; Transformer design and analysis

Additional Info: If coils are placed at right angles to each other, the coefficient of coupling becomes zero.. Option A and B are incomplete because the coupling coefficient is essentially a ratio relating all three variables.

Answer: C is correct — The coefficient of coupling is defined as the ratio of mutual inductance to the geometric mean of the self-inductances of the two coils.

Exam Tip: In competitive exams, remember that $k$ is always $\le 1$. If a question asks about coils in series, use the relation $L_{eq} = L_1 + L_2 \pm 2M$ to relate $M$ to $k$.

Examoogle · Answer

Option A: Self-inductance of two coils only

Examoogle · Answer

Option B: Mutual inductance between two coils only

Examoogle · Answer

Option D: None of above

Correct Answer

Discussion (0)

Correct Answer

Related Questions

Discussion (0)