1. ECE 201 Circuit Theory 11 Energy Calculations for Mutually – Coupled Coils

2. ECE 201 Circuit Theory 12 Energy Calculations continued To begin, assume that currents i 1 and i 2 are equal to zero Let current i 1 increase to a value I 1 Compute the energy stored

3. ECE 201 Circuit Theory 13 Energy Calculations Continued Hold i 1 constant and increase i 2 to I 2 Voltage induced in L 2 by I 1 = 0 Voltage induced in L 1 by i 2 = M 12 (di 2 /dt)

4. ECE 201 Circuit Theory 14 Power Input to the pair of coils

5. ECE 201 Circuit Theory 15 If the procedure were reversed When the medium is linear, M 21 = M 12, and the total energy stored is the same!

6. ECE 201 Circuit Theory 16 Instantaneously This case had both currents entering a dotted terminal. If one current enters a dotted terminal and the other current leaves a dotted terminal, the sign of the Mi 1 i 2 term reverses.