Choosing meter polarities:
Remember that when you annotate a wire with a "current definitional arrow"
you are implicitly inserting a ammeter (current meter) into the circuit
at that point. Your arrow shows the direction of current flow that will
cause your meter to read a positive number. If you write a variable name
by the arrow (e.g. i3), this means that the value of
the variable will be positive when current flows in the direction of the
arrow, and negative when current flows opposite to the arrow.
It is totally up to you how to draw the current definitional arrow.
It is customary, if you can guess which way the current really will flow,
to draw the arrow in the directon of the actual current flow, so that when
you later solve for the associated variable it will turn out to have a
positive value. However sometimes the current oscillates, and sometimes
it's steady but you can't tell which direction it will flow, and sometimes
you guess wrong, and sometimes you are just in a perverse mood and draw
it backwards on purpose. No problem. It doesn't matter.
What does matter is that, once you have chosen the current definitional
arrows, you must draw the voltmeter polarities consistently with the current
definitional arrows. If you don't, the constitutive laws that you later
use will be wrong - they will have sign errors. Here are the rules for
assigning voltmeter polarity:
For resistors, capacitors, inductors, and all elements other than voltage
sources (e.g. batteries), make sure that when the current is positive (as
defined by the current definitional arrow) that the "+" side of the voltmeter
For batteries, ignore the current definitional arrow. Always connect
the "+" side of the voltage meter to the positive end of the battery.