1. Mutual Inductance
Consider two circuits “linked” by a magnetic field (magnetically-coupled coils).
ECE 201 Circuit Theory I

2. “Self-Inductances” are L1 and L2. The “Mutual” Inductance is M.
The voltage induced in one circuit is related to the time-varying current in the other circuit.
ECE 201 Circuit Theory I

3. Analysis
Easiest with mesh-current method.
ECE 201 Circuit Theory I

4. Write the circuit equations in terms of the coil currents.
Arbitrarily assign the current directions.
There will be two voltages across each coil, the “self-induced” voltage, L(di/dt), and a “mutually induced” voltage, M(di/dt).
ECE 201 Circuit Theory I

5. Determination of Voltage Polarities
“Dot convention”
Dots indicate the direction in which the coils are wound.
ECE 201 Circuit Theory I

6. The Rule for using the Dot Convention
When the reference direction for a current enters the dotted terminal of a coil, the reference polarity of the voltage that it induces in the other coil is positive at its dotted terminal.
ECE 201 Circuit Theory I

7. Alternate Rule for the Dot Convention
When the reference direction for a current leaves the dotted terminal of a coil, the reference polarity of the voltage that it induces in the other coil is negative at its dotted terminal.
ECE 201 Circuit Theory I

8. For this Example
The voltage induced in coil 1 by the current in coil 2 is negative at the dotted terminal of coil 1, and is a voltage rise with respect to current i1.
ECE 201 Circuit Theory I

9. For this Example
The voltage induced in coil 2 by the current in coil 1 is positive at the dotted terminal of coil 2, and is a voltage rise with respect to current i2.
ECE 201 Circuit Theory I

10. Write the Mesh Equations
ECE 201 Circuit Theory I

11. Example 6.6, page 206
Write a set of mesh equations that describe the circuit shown in terms of i1 and i2.
ECE 201 Circuit Theory I

12. ECE 201 Circuit Theory I

13. ECE 201 Circuit Theory I