Assigning Polarities and using them in KVL equation, circuits

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Assigning polarities in circuit analysis is crucial for applying Kirchhoff's Voltage Law (KVL) correctly. When analyzing components like resistors, the polarity can be assigned based on the assumed direction of current flow, with consistent assignment being key. For batteries connected in series, the total voltage is the sum of individual voltages, while in parallel configurations, the voltage across each branch remains the same. When applying KVL, a voltage rise is considered positive when moving from negative to positive polarity, and a drop is negative when moving from positive to negative. Ultimately, consistency in polarity assignment ensures accurate results in circuit calculations.
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I am having trouble understanding how to assign polarities to voltage when it goes through components of a circuit and how those polarities determine the sign of the quantities I put in the KVL equation. Attached is a picture of a circuit. The points where polarity matters are labeled 1-14. I am trying to find the voltage of battery 1/2. I know how to assign polarities to batteries but are there any rules I should obey when assigning polarities to resistors? Also what happens to voltage when batteries are connected like battery 1/2 and battery 3/4 in the picture? Also when putting quantities in the kvl equation how can I determine which quantity is positive and which is negative? and lastly what role do polarities play when solving circuit problems?
 

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It doesn't matter as long as you are consistent. If you guess wrong all that will happen is that when you solve the system of equations one of the voltages will be negative.
 
if you assign all +/- pairs consistently going around the loop, the sum of the voltages must equal zero.

but if you assign the polarities as you see fit, then, going around the loop (either clockwise or counter-clockwise), then KVL says that the sum of the voltage rises equals the sum of the voltage drops.

both versions say the same thing.
 
ok so when putting the voltages in the equation how do I distinguish between the two different polarities? another way to say this is how to I know when the voltage drops and when the voltage rises?
 
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