# Circuit with Coupled Inductance

The figure below shows the circuit from Example 11.9-1 of Introduction to Electric Circuits, 5e by R.C. Dorf and J.A. Svoboda. This circuit contains coupled coils. These coils are represented by three parameters: the primary inductance L1, the secondary inductance L2 and the mutual inductance M. (The primary coil is the coil on the left. The secondary coil is on the right.) The coupling coefficient, k, of coupled coils is defined as

The coupling coefficient must satisfy .

The steady state response of this circuit is given by

The values of the inductances L1 and L2 of the coupling coefficient k can be changed using the scrollbars. Notice that the circuit diagram is labeled using the value of the mutual inductance M calculated from L1, L2 and k.

Suggestions:

1. Set L1=4 H, L2 = 3 H and k=0.58 to see the circuit in Example 11.9-1.

2. Set L1=6 H, L2 = 8 H and vary k. Watch M change as k changes. What is the range of values of M corresponding to ? Predict the value of k required to obtain M=6 H. Use the scrollbars to check this prediction.

3. Set L1=9 H, k = 1 and vary L2. Watch M change as L2 changes. What is the range of values of M corresponding to ? Predict the value of L2 required to obtain M=8 H. Use the scrollbars to check this prediction.

4. Use the scrollbars to select values of L1, L2 and k such that . Verify the values of L1, L2 and k using the given equations.