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Question: Initially the switch position is aa', 3 H is connected across a 3 A supply and 6 H is connected across 6 A supply. After some time the make before break switch is actuated to the new position bb'. Determine the steady state current, fluxes associated with each inductor in the new position. Assume there are no switching losses. Fig 1 : Initial condition (switch in aa') Fig 2: circuit while operating the make before break switch Fig 3 : switch in bb'

Pre switching period is fine, each inductor having a current of 3 A and 6 A respectively. Inductors don't allow a sudden change in current when disconnected from supply as in fig 3, their magnetic field collapses and allow a decreasing current to flow in the same direction as previous and their voltages are reversed. But how does it behave when two inductors having different initial currents are switched together? It shouldn't be 9 A otherwise total energy associated with the series inductors is more than pre switching violating law of conservation of energy. Is this case similar to connecting two current sources in series which is not allowed?

circuit

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  • \$\begingroup\$ What are your thoughts? In a series circuit you can't have different currents in each component and you can't change the current in an inductor in zero time. \$\endgroup\$ – Warren Hill Jul 26 '18 at 10:15
  • \$\begingroup\$ When two inductors \$L_1\$ and \$L_2\$ , with initial currents \$I_{0_1}\$ and \$I_{0_2}\$, come in series, the equivalent inductance becomes \$L_{eq}\$=\$L_1\$+\$L_2\$, and the equivalent initial current \$I_{t_0}=\frac{L_1I_{0_1}+L_2I_{0_2}}{L_1+L_2}\$, derived from \$\phi=LI\$. The voltage of each inductor can change whatever it needs to be to make the current almost suddenly change. \$\endgroup\$ – dirac16 Jul 26 '18 at 10:33
  • \$\begingroup\$ Huh? What are those weird things labeled a, b, a', and b'? \$\endgroup\$ – Olin Lathrop Jul 26 '18 at 10:44
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    \$\begingroup\$ C'mon guys, they are clearly make before break switches however, the hand drawn fig 2 is misleading because it doesn't represent the final circuit. \$\endgroup\$ – Andy aka Jul 26 '18 at 11:44
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    \$\begingroup\$ An arc will always occur even in an ideal vacuum. Two opposite currents switched with 0V steady state will be like shorting 2 ideal caps charged to some opposite voltage but different energy stored . \$\endgroup\$ – Sunnyskyguy EE75 Jul 26 '18 at 11:44

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