Two coils `A` and `B` having turns `300` and `600` respectively are placed near each other, on passing a current of `3.0` ampere in `A`, the flux linked with `A` is `1.2xx10^(-4)` and with `B` it is `9.0xx10^(-5)` weber. The mutual inuctance of the system is

Options

A. `2xx10^(-5)H`
B. `3xx10^(-5)H`
C. `4xx10^(-5)H`
D. `6xx10^(-5)H`

Answer

To find the mutual inductance of the system formed by coils A and B, we can follow these steps:

### Step 1: Understand the relationship between flux and mutual inductance
The mutual inductance \( M \) between two coils is defined by the equation:
\[ \Phi_2 = M \cdot I_1 \]
where:
- \( \Phi_2 \) is the flux linked with coil B,
- \( I_1 \) is the current flowing through coil A,
- \( M \) is the mutual inductance.

### Step 2: Identify the given values
From the problem, we have:
- The flux linked with coil B, \( \Phi_2 = 9.0 \times 10^{-5} \) Weber,
- The current in coil A, \( I_1 = 3.0 \) Ampere.

### Step 3: Rearrange the equation to solve for mutual inductance \( M \)
We can rearrange the equation to find \( M \):
\[ M = \frac{\Phi_2}{I_1} \]

### Step 4: Substitute the known values into the equation
Now, substituting the known values into the equation:
\[ M = \frac{9.0 \times 10^{-5}}{3.0} \]

### Step 5: Perform the calculation
Calculating the above expression:
\[ M = 3.0 \times 10^{-5} \text{ Henry} \]

### Conclusion
Thus, the mutual inductance of the system is:
\[ M = 3.0 \times 10^{-5} \text{ Henry} \]