Coefficient of coupling between two coils of self-inductances `L_(1)` and `L_(2)` is unity. It means

Options

A. `50%` flux of `L_(1)` is linked with `L_(2)`
B. `100%` flux of `L_(1)` is linked with `L_(2)`
C. `sqrt(L_(1))` time of flux of `L_(1)` is linked with `L_(2)`
D. None of the above

Explanation

To solve the problem regarding the coefficient of coupling between two coils of self-inductances \(L_1\) and \(L_2\) being unity, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Coefficient of Coupling**:
The coefficient of coupling \(k\) between two coils is defined as the ratio of the mutual inductance \(m\) to the geometric mean of the self-inductances \(L_1\) and \(L_2\):
\[ k = \frac{m}{\sqrt{L_1 L_2}} \]

2. **Given Condition**:
We are given that the coefficient of coupling \(k\) is unity:
\[ k = 1 \]

3. **Setting Up the Equation**:
Substituting \(k = 1\) into the equation gives:
\[ 1 = \frac{m}{\sqrt{L_1 L_2}} \]

4. **Cross Multiplying**:
Cross-multiplying the equation leads to:
\[ m = \sqrt{L_1 L_2} \]

5. **Interpreting the Result**:
The equation \(m = \sqrt{L_1 L_2}\) indicates that the mutual inductance \(m\) is equal to the geometric mean of the self-inductances \(L_1\) and \(L_2\). This situation occurs when all the magnetic flux produced by one coil links perfectly with the other coil.

6. **Conclusion**:
When the coefficient of coupling is unity, it signifies that 100% of the magnetic flux from one coil links with the other coil. This is the maximum possible coupling between two coils.

### Final Answer:
The coefficient of coupling being unity means that 100% of the magnetic flux from coil \(L_1\) is linked with coil \(L_2\).

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