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Consider the crosshatched current-carrying wires depicted:

crosshatched

The shorter wires have been placed on top of the longer wires. Each wire can facilitate a maximum of 170 amperes of current and contributes a small amount of resistance to the circuit. Note that wires carrying 170 A are parts of separate circuits that include more elements than the wires depicted (e.g., a battery).

Since the conductors are touching, is there any way to predict how current will flow across the ‘bridge’ that is formed?

If more information about these circuits is needed to formulate an answer, please share that in the comments.

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  • \$\begingroup\$ Is your purpose to spread out the load, to avoid burning up wires? \$\endgroup\$ – analogsystemsrf Jun 15 '17 at 4:09
  • \$\begingroup\$ @analogsystemsrf Precisely! I also need to maintain a rectangular shape marked by parallel sides and 90° angles. \$\endgroup\$ – Chase Ryan Taylor Jun 15 '17 at 4:10
  • \$\begingroup\$ Each length of wire can be modeled as a resistor whose resistance is proportional to its length. I mean the length to the crossing point. The actual resistance can be calculated using the bulk resistivity of the conductor. I would suggest you load it into spice and see what happens. However, in order to find out how much current is flowing you will need to supply the whole circuit. \$\endgroup\$ – mkeith Jun 15 '17 at 4:35
  • \$\begingroup\$ @mkeith Will the current divide itself evenly through the two wires? That's more my focus \$\endgroup\$ – Chase Ryan Taylor Jun 15 '17 at 4:36
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    \$\begingroup\$ the resistances will not be identical because the lengths are not identical. Calculate the resistance of each segment of wire, proportional to its length. \$\endgroup\$ – Neil_UK Jun 15 '17 at 5:00
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To a first approximation, assume the two wires of the each pair are near, and the out and return pairs are far apart. In the limit, when near/far = 0, each junction in the group of 4 crossings has the same voltage, and each wire will carry 170A.

To see what's going to happen when the spacings are significant, the resistance of the wire, and the current flowing through it, creates a voltage drop on the spacing between the two wires in each pair, proportional to their spacing and resistivity. This means that a higher current flows in the 'inner' wire of each pair. The wider the intra-pair spacing compared to the inter-pair spacing, the larger the imbalance.

It's worth pointing out that in a real experiment, the contact resistances may well be more significant then the resistance of the wire. These would tend to dominate the wire length resistance, and tend to equalise the currents. They would also be very pressure dependant, and make an experiment unstable and difficult to measure.

It's quite easy to solve for the exact currents, once resistances, including contact resistances, have been specified. We also need to specify what's driving the 170A, whether it's a current source, or a voltage source and some source/load resistance.

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  • \$\begingroup\$ I will leave this question open for the rest of the day. If no one else answers I will give this the green check. Excellent point about the contact resistance; I had not considered that, and we never discussed it in class. \$\endgroup\$ – Chase Ryan Taylor Jun 15 '17 at 5:59

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