VIR chart for circuit analysis with two batteries

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stephen8686
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Hello guys,
I'm reviewing for the AP physics C exam and in one of my review books I came across this trick called a VIR chart for circuit analysis. It's a sort of weird alternative to the usual Loop Rule. If you haven't heard of it before here it is: https://jacobsphysics.blogspot.com/2009/03/i-got-email-from-geoff-clarion-other.html?m=1

I found this to be much quicker and more intuitive than the loop rule usually is but I'm not sure how it could be done with a two-battery circuit. I suppose it can't be used with rc or rl circuits either?
 
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The idea seems to be to simplify the problem by first calculating resistances within the circuit using the parallel and series formulae. That's not different from using the two Kirchhoff Laws, it's sometimes just a short cut.