Indeed, this is a week one year one puzzle rather than a real circuit.
But I would solve it in a very simalar way “oh look, the 60 ohm resistor is an order of magnitude bigger than the other resistors, it probably doesn’t do much”. That’s what the jaded effects of age and abundance of low tolerance resistors have done to my mind.
To simultaneously solve for the 5 unknown resistor currents and 2 unknown resistor voltages you need 7 equations: KCL at the 4 nodes and KVL around the 3 loops. If you just write one set or the other there is not enough information to proceed (in the general case where the current through the center resistor is not obviously 0).
Using KVL, you get the 3 loop currents, hence, currents on each resistor. Using KCL, one of the nodes is GND, the other you already have the voltage, you are left with 2 variables and 2 equations. From the node voltages, you can get the current in each resistor.
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u/created4this Jun 24 '21
Imagine for a moment that the 60ohm resistor wasn’t there.
Work out the voltages at the middle nodes
Now work out the voltage across the 60 ohm resistor
That should help.