# Analyzing a rail design circuit that must have constant current?

I'm designing a circuit for the diagram below:

Where a mechanical source will move the rod. During the rod's change in position the direct current must be constant ($I_c$) from $t_i$ to $t_f$. When I analyze the change, I observe that the current's path will increase, due to the two horizontal wires increasing in length, and if we considered the resistances of the R + R(rod) + R(wires), $R_t$ will increase(the magnitude will depend on the length). In order to maintain constant current, the applied voltage must change, therefore, a constant current source(CCS) would be an ideal solution.

I also think that the inductance of the circuit) will increase(not sure).

At the start of the process, current is at it's maximum value and the circuit is in a steady state, as the rod begins to move and $R$ & $L$ increase, will a constant current source(CCS) maintain $I_c$ throughout the process? Also, how will the increased inductance affect the CCS/or the circuit( self inductance)?

I'm confused as how current can stay constant using a CCS while $R$ & $L$ increase, aside from the input power increasing for the higher voltage, what else would I need to consider?

• I used to give this exact question as a homework assignment. – Seth Sep 19 '16 at 21:07
• Well, that's interesting! Were the HW problems related/about rail guns? This design is the same, however, I'm not trying to use the Lorentz force at all, also the required current is low. It's a possible solution for a ME project I have in mind. – Pupil Sep 19 '16 at 21:11
• I fail to see how this doesn't use the Lorentz force. Low current=low force=rod doesn't move due to friction. – Seth Sep 19 '16 at 21:24
• That is true, however, I plan to change the design more. The goal is to have current(in that rod) constant while mechanically moving it in any position $-x/x$. In-terms of friction, I have a couple of options, however, I assure you it will move. – Pupil Sep 19 '16 at 22:26

It seems to me that if you use a CCS as your power supply you will have a diagram as follows:

simulate this circuit – Schematic created using CircuitLab

The voltage across the rod will be constant but the voltage across the terminals of the CCS will be slightly different depending on the position of the rod.

as the rod begins to move and R & L increase, will a constant current source(CCS) maintain Ic throughout the process?

As long as your CCS is good at regulating current, then yes. The key is to know how the CCS is generating its current. Just like CVS, they must have a regulation loop to maintain constant current across a range of voltages.

how will the increased inductance affect the CCS/or the circuit( self inductance)?

In steady-state, the (potentially small) change in inductance will have no effect on the voltage or current through the rod. However, if the rod were to move suddenly and quickly (high dI/dt), then the voltage across the CCS will spike to accommodate the changing inductance. This effect will become more pronounced as the loop inductance increases.

• From V = L*dI/dt, if the rod moved rapidly the induced EMF will resist that decrease in change, making it $V_p$ + $V_E$ ? Where $V_p$ is the applied voltage, and $V_E$ the induced EMF. – Pupil Sep 20 '16 at 0:45
• Theoretically, yes. In reality, the CCS will not have infinite regulation bandwidth and depending on how much faster the induced EMF is, there could be a combination of voltage and current fluctuation until the circuit reaches steady-state again – Daniel V Sep 20 '16 at 16:51