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What is the coefficient of mutual inductance, when the magnetic flux changes by 2X10-2 Wb and change in current is 0.01 A ?
- a)2 henry
- b)3 henry
- c)1/2 henry
- d)Zero
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
What is the coefficient of mutual inductance, when the magnetic flux c...
L = e / (di / dt) (:. e = dΦ / dt) L =(dΦ / dt) / (di / dt) L = dΦ / diL = 2 × 10^ -2 /0.01. L = 2 henry
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What is the coefficient of mutual inductance, when the magnetic flux c...
To determine the coefficient of mutual inductance (M), we can use the formula that relates the change in magnetic flux (Φ) through one coil to the change in current (I) in another coil. The formula is:
Mutual Inductance Formula
\[
M = \frac{\Delta \Phi}{\Delta I}
\]
Where:
- \( \Delta \Phi \) = Change in magnetic flux (in Weber, Wb)
- \( \Delta I \) = Change in current (in Ampere, A)
Given Values
- \( \Delta \Phi = 2 \times 10^{-2} \, \text{Wb} \)
- \( \Delta I = 0.01 \, \text{A} \)
Substituting the Values
Now, substitute the given values into the formula:
\[
M = \frac{2 \times 10^{-2} \, \text{Wb}}{0.01 \, \text{A}}
\]
Calculating the Coefficient
Perform the calculation:
\[
M = \frac{2 \times 10^{-2}}{0.01} = \frac{2 \times 10^{-2}}{1 \times 10^{-2}} = 2 \, \text{H}
\]
Thus, the coefficient of mutual inductance \( M \) is 2 Henry.
Conclusion
The correct answer is option A (2 Henry). This indicates that a change in current of 0.01 A results in a change in magnetic flux of 2 x 10^-2 Wb, confirming the relationship defined by mutual inductance.
Mutual Inductance Formula
\[
M = \frac{\Delta \Phi}{\Delta I}
\]
Where:
- \( \Delta \Phi \) = Change in magnetic flux (in Weber, Wb)
- \( \Delta I \) = Change in current (in Ampere, A)
Given Values
- \( \Delta \Phi = 2 \times 10^{-2} \, \text{Wb} \)
- \( \Delta I = 0.01 \, \text{A} \)
Substituting the Values
Now, substitute the given values into the formula:
\[
M = \frac{2 \times 10^{-2} \, \text{Wb}}{0.01 \, \text{A}}
\]
Calculating the Coefficient
Perform the calculation:
\[
M = \frac{2 \times 10^{-2}}{0.01} = \frac{2 \times 10^{-2}}{1 \times 10^{-2}} = 2 \, \text{H}
\]
Thus, the coefficient of mutual inductance \( M \) is 2 Henry.
Conclusion
The correct answer is option A (2 Henry). This indicates that a change in current of 0.01 A results in a change in magnetic flux of 2 x 10^-2 Wb, confirming the relationship defined by mutual inductance.
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