Question

Find the coefficient of mutual inductance of a pair of coils if a current of 3 A in one coil causes the flux in the second coil of 1000 turns to change by \( 10^{-4} \, \text{weber} \) in each turn.

Hint:

The mutual inductance between two coils can be found using the flux linkage in the second coil and the current in the first coil.

Answer 1

Step 1: Formula for mutual inductance.
The mutual inductance \( M \) between two coils is defined as the ratio of the flux linkage in one coil due to a current in the other coil. The flux linkage in the second coil is given by: \[ \Phi_2 = M \cdot I_1 \] where:
- \( M \) is the mutual inductance, - \( \Phi_2 \) is the total flux linked with the second coil, - \( I_1 \) is the current in the first coil.
The total flux in the second coil is the flux in each turn multiplied by the number of turns \( N_2 \): \[ \Phi_2 = N_2 \cdot \Phi_{\text{turn}} \] where \( \Phi_{\text{turn}} \) is the flux in one turn of the second coil.
Step 2: Substituting the given values.
We are given: - \( I_1 = 3 \, \text{A} \), - \( N_2 = 1000 \) turns, - \( \Phi_{\text{turn}} = 10^{-4} \, \text{weber} \).
Using the above formulas: \[ \Phi_2 = 1000 \times 10^{-4} = 10^{-1} \, \text{weber} \] Now, using the formula for mutual inductance: \[ M = \dfrac{\Phi_2}{I_1} \] \[ M = \dfrac{10^{-1}}{3} = 3.33 \times 10^{-2} \, \text{H} \] Step 3: Conclusion.
The coefficient of mutual inductance between the coils is \( 3.33 \times 10^{-2} \, \text{H} \).