Voltage Division

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The third IET panel task is replicated here. The challenge is to combine resistors to divide down 12 V DC to a target voltage.

You may assume the resistors have zero tolerance.

You must ensure both the positive 12 V and 0 V are connected to resistors. You can then probe voltages at different network points using the multimeter.

The networks that solves the puzzles will generally require only a few resistors, but the network can be made arbitrarily complex. You can select jumper wire colours using the colour block (at the bottom of the canvas) for clarity if the network is elaborate.

However, you should try to start with simple series and parallel pairs and combinations.

Remember, resistors in series add and, in parallel, the total resistance is the product divided by the sum. The voltage registered on the multimeter is the ratio of the total resistance to ground allong all paths divided by the total resistance between supply rails.

You will quickly notice that trial-and-error is rather ineffective. You may choose to investigate all 2, 3 and 4 resistor combinations using a spreadsheet to guide you.

Because the network can be arbitrarily complex, the software identifies all the unique nodes and assigns an initial voltage to nodes not connected directly to the power rails. By calculating the total current into each node (which should be zero when the node voltages are correct), a small correction may be made to the voltage. By this process (replicating what happens in a real circuit when the circuit is closed), the voltage converges to a stable value. 100 iterations are allowed before the process terminates. If full convergence is not achieved, a warning message is displayed.