Paralell Inductors in a DC Circuit with Constant Current

[Peddler1010]

Hi,

This isn't so much of a home work problem just a request for clarification from those that are more intelligent than I. I actually just wrote the final for Basic Circuit Analysis and there was a question that left me totally stumped.

I've attached a VERY crude, much less complicated version of the question..er..in question.

We were given a network of inductors and asked to find the equivalent inductance between a particular set of terminals. Easy enough. We were then asked to find the energy stored in each individual inductor if a 2A current source is attached between the terminals.

My question then, is this (Have a look at the diagram): Since inductors act like short circuits in DC when at their steady state, can I (as I did in the exam) assume that the current from the source (I1) splits evenly through the two branches. So if I1 is 1A, then L3 sees .5 Amps and L1 and L2 both share .5A. Since they are in parallel they would both see .25 A.

And then w = (1/2)*L*i^2 for each of the L's with their respective i's.

Is that even close to correct? The question was a lot more complicated than the simple version that I showed you here, but it was worth like 5/100, so I can't see the solution being that tough.

Anyway, I would really appreciate even just a Yes or No answer to this.

Thanks Alot.

 

[berkeman]

Hi,

This isn't so much of a home work problem just a request for clarification from those that are more intelligent than I. I actually just wrote the final for Basic Circuit Analysis and there was a question that left me totally stumped.

I've attached a VERY crude, much less complicated version of the question..er..in question.

We were given a network of inductors and asked to find the equivalent inductance between a particular set of terminals. Easy enough. We were then asked to find the energy stored in each individual inductor if a 2A current source is attached between the terminals.

My question then, is this (Have a look at the diagram): Since inductors act like short circuits in DC when at their steady state, can I (as I did in the exam) assume that the current from the source (I1) splits evenly through the two branches. So if I1 is 1A, then L3 sees .5 Amps and L1 and L2 both share .5A. Since they are in parallel they would both see .25 A.

And then w = (1/2)*L*i^2 for each of the L's with their respective i's.

Is that even close to correct? The question was a lot more complicated than the simple version that I showed you here, but it was worth like 5/100, so I can't see the solution being that tough.

Anyway, I would really appreciate even just a Yes or No answer to this.

Thanks Alot.

Welcome to the PF. For DC, inductor currents need to be defined by something other than their inductance. Either their DCR, or some other rresistors somewhere in the circuit, or something would have to define it. Having two ideal inductors in parallel being fed by a current source, there is no way I know of to determine how the current might divide.

Maybe you could ramp the current up at some rate, which would give you current division according to their inductances, and then argue that when there is no change in current at the DC top of the ramp, the two currents will stay constant, at that divide ratio? Hmm, maybe try that math to see if it works out. But that only works if there is an initial transient aspect to the current source. Although maybe that can be assumed, since the circuit had to be turned on at some point in the history of time...

 

[Mene]

Hi there,

Yes, your approach to splitting the current evenly between the two branches is correct. In a DC circuit with constant current, the inductors act as short circuits and the current is divided evenly between them. This means that each inductor will experience the same amount of current and will store the same amount of energy, as you have calculated using the equation w = (1/2)*L*i^2.

However, it is important to note that this only applies to a DC circuit with constant current. If the circuit were to have varying current, the inductors would not act as short circuits and the current would not be divided evenly between them. The energy stored in each inductor would also vary depending on the current at any given time.

I hope this helps clarify your understanding. Keep up the good work!