Question

The equivalent inductance of two equal inductances when connected in series aiding is 14 H and when connected in series opposing is 6 H. What is the coefficient of coupling?

• A. 0.5
• B. 0.8
• C. 0.4
• D. 1.0

Hint:

Use \( L_{\text{aiding}} = 2L + 2M \) and \( L_{\text{opposing}} = 2L - 2M \) for coupled inductors and solve for \( M \) and then \( k = \frac{M}{L} \).

Answer 1

The Correct Option is C

For two equal inductances \( L \) with mutual inductance \( M \): \[ L_{\text{series aiding}} = 2L + 2M = 14 \] \[ L_{\text{series opposing}} = 2L - 2M = 6 \] Adding both: \[ (2L + 2M) + (2L - 2M) = 14 + 6 \] \[ 4L = 20 \Rightarrow L = 5\, H \] Now, using one equation: \[ 2(5) + 2M = 14 \] \[ 10 + 2M = 14 \Rightarrow 2M = 4 \Rightarrow M = 2\, H \] Then, the coefficient of coupling \( k \) is: \[ k = \frac{M}{L} = \frac{2}{5} = 0.4 \]