Question

The coefficient of coupling is \(0.8\). If the mutual inductance is \(8\ \text{H}\), then the values of self-inductances \(L_{1}\) and \(L_{2}\) of the coil are

• A. \(60\ \text{H}\) and \(40\ \text{H}\)
• B. \(90\ \text{H}\) and \(10\ \text{H}\)
• C. \(5\ \text{H}\) and \(20\ \text{H}\)
• D. \(5\ \text{H}\) and \(10\ \text{H}\)

Hint:

Use k equals M over root of L1 L2 to find the product of the self-inductances, then test the option pairs.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
The coefficient of coupling is \(k=\dfrac{M}{\sqrt{L_{1}L_{2}}}\).

Step 2: Find the product
\(\sqrt{L_{1}L_{2}}=\dfrac{M}{k}=\dfrac{8}{0.8}=10\ \text{H}\), so \(L_{1}L_{2}=100\ \text{H}^{2}\).

Step 3: Test the options
(A) \(60\times40=2400\), (B) \(90\times10=900\), (C) \(5\times20=100\), (D) \(5\times10=50\).

Step 4: Result
Only \(5\ \text{H}\) and \(20\ \text{H}\) give a product of 100.

Final Answer:
The self-inductances are 5 H and 20 H. \[ \boxed{\text{(C) }\text{5 H and 20 H}} \]