Energy storage of two parallel inversely connected coupling coils

Wang Yongzhong

(Institute of Metal Research, Chinese Academy of Sciences)

(yzhwang@imr.ac.cn)

1、Consumption of power supply in a

pure resistive circuit

Connect a pure resistance circuit with the power supply, then the current in the circuit immediately rises to a stable value I=E/R, where E is the electromotive force of the power supply and R is the resistance. The consumption of the power supply is the joule heat I²R generated by resistance.

2、consumption of power supply in an

L-R circuit

When the L-R circuit is connected to the electromotive force E of the power supply, the current in the circuit does not rise to a stable value E/R immediately^[1]. The relationship between current and time is ， where τ=L/R is the time constant. The reason is that the change in the current in the coil produces a self-induced electromotive force in the opposite direction to the power supply electromotive force. The power supply electromotive force must overcome this self-induced electromotive force to make the current rise. In this process the power supply electromotive force overcomed the self-induced electromotive force to do work and make the coil store energy.  

This indicates that if there was a steady current in an L-R circuit is I, then the magnetic energy （1/2）L I² must be stored in the coil of self-inductance L. In this case, the power consumption is the sum of the magnetic energy stored in the coil and the joule heat generated by the resistance （1/2）L I²+I²R.

3、Magnetic energy stored in two tightly coupled coils connected in parallel

Tightly coupled coils 1 and 2 have self-inductance (L) and mutual inductance (M) , and L equal to M.  Connect the

two coils in parallel inversely, according to electromagnetism theory the equivalent inductance of the system composed of two coils is zero, that is, it is a pure resistance^[2].

Now connect the two-coil system to the power supply,

and the current of the system immediately rises to a stable

value  I=2E/R，the current in each coil also immediately rises to a steady value I=E/R，where R is the coil resistance.

At the same time, magnetic energy (1/2 L I²) was stored in the each coils, where L is the coil self-induction coefficient.

It's worth noting that，although magnetic energy was stored in the two coils, but the consumption of power is only  joule heat 2I²Rt generated by the resistance, where t is the energized time.  

4、 Output of magnetic energy in a coils

 As long as the coil were not disconnected from the power supply at the same time, the energy storage in the coil can be output to the load.  

References

1  Zhao kaihua  Chen ximou. New concept physics (electromagnetism)（Higher Education Press ，beijing，2003）189

2  Wen shengle. About the connection of inductor coils. college physics，2005,24（07）12（https://wenku.baidu.com/view/0fa07154eefdc8d376ee32e3.html）