Question:
Two coils having self-inductances \(\mathrm{L}_1=75 \mathrm{mH}\) and \(L_2=48 \mathrm{mH}\) are coupled with each other. If the mutual inductance of the coils is 37.2 mH , then coefficient of coupling will be
Two coils having self-inductances \(\mathrm{L}_1=75 \mathrm{mH}\) and \(L_2=48 \mathrm{mH}\) are coupled with each other. If the mutual inductance of the coils is 37.2 mH , then coefficient of coupling will be
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Coefficient of coupling is the mutual inductance divided by the geometric mean of the two self-inductances.
Updated On: Nov 13, 2026
0.58
0.60
0.62
0.64
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept
The coupling coefficient is \(k = \dfrac{M}{\sqrt{L_1 L_2}}\).
Step 2: Substitute the Values
\(L_1 = 75\ \text{mH}\), \(L_2 = 48\ \text{mH}\), \(M = 37.2\ \text{mH}\)
\(\sqrt{L_1L_2} = \sqrt{75\times 48} = \sqrt{3600} = 60\ \text{mH}\)
Step 3: Calculation
\(k = \dfrac{37.2}{60} = 0.62\)
Step 4: Compare the options
0.62 matches option C.
Final Answer:
The coefficient of coupling is 0.62. \[ \boxed{\text{(C) }0.62} \]
The coupling coefficient is \(k = \dfrac{M}{\sqrt{L_1 L_2}}\).
Step 2: Substitute the Values
\(L_1 = 75\ \text{mH}\), \(L_2 = 48\ \text{mH}\), \(M = 37.2\ \text{mH}\)
\(\sqrt{L_1L_2} = \sqrt{75\times 48} = \sqrt{3600} = 60\ \text{mH}\)
Step 3: Calculation
\(k = \dfrac{37.2}{60} = 0.62\)
Step 4: Compare the options
0.62 matches option C.
Final Answer:
The coefficient of coupling is 0.62. \[ \boxed{\text{(C) }0.62} \]
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