Question:
A pair of adjacent coils having a mutual inductance \(M\). The current in one coil changes from \(0\) to \(16\,\text{A}\) in \(0.3\,\text{s}\) and the change of flux linkage with the other coil is \(40\,\text{Wb}\). The value of \(M\) is
A pair of adjacent coils having a mutual inductance \(M\). The current in one coil changes from \(0\) to \(16\,\text{A}\) in \(0.3\,\text{s}\) and the change of flux linkage with the other coil is \(40\,\text{Wb}\). The value of \(M\) is
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Mutual inductance relates flux linkage in one coil to current in the other coil:
\[
M=\frac{\Delta \lambda}{\Delta I}.
\]
The time interval is needed only when induced emf is asked.
Updated On: Jun 18, 2026
- \(0.4\,\text{H}\)
- \(0.12\,\text{H}\)
- \(2.5\,\text{H}\)
- \(8.3\,\text{H}\)
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The Correct Option is C
Solution and Explanation
Step 1: Use the definition of mutual inductance.
Mutual inductance is defined as \[ M=\frac{\Delta \lambda}{\Delta I} \] where \(\Delta \lambda\) is the change in flux linkage and \(\Delta I\) is the change in current.
Step 2: Write the given values.
The change in flux linkage is \[ \Delta \lambda=40\,\text{Wb} \] The current changes from \(0\) to \(16\,\text{A}\), so \[ \Delta I=16-0 \] \[ \Delta I=16\,\text{A} \]
Step 3: Calculate mutual inductance.
\[ M=\frac{40}{16} \] \[ M=2.5\,\text{H} \]
Step 4: Final conclusion.
Therefore, the value of mutual inductance is \[ \boxed{2.5\,\text{H}} \]
Mutual inductance is defined as \[ M=\frac{\Delta \lambda}{\Delta I} \] where \(\Delta \lambda\) is the change in flux linkage and \(\Delta I\) is the change in current.
Step 2: Write the given values.
The change in flux linkage is \[ \Delta \lambda=40\,\text{Wb} \] The current changes from \(0\) to \(16\,\text{A}\), so \[ \Delta I=16-0 \] \[ \Delta I=16\,\text{A} \]
Step 3: Calculate mutual inductance.
\[ M=\frac{40}{16} \] \[ M=2.5\,\text{H} \]
Step 4: Final conclusion.
Therefore, the value of mutual inductance is \[ \boxed{2.5\,\text{H}} \]
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