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Kirchhoff's Voltage Law

Kirchhoff’s Voltage Law states that the total voltage around a closed loop must be zero. This is the result of the electrostatic field being conserved. If Kirchhoff’s Law were not true, then we would travel around a closed loop and the voltage would be indefinite.

∑V = 0

The Kirchhoff’s voltage equation is obtained by traversing a circuit loop in either direction and writing down unchanged the voltage of each element whose “+” terminal is entered first and writing down a negative of every element’s voltage where the minus sign is met. The loop must state and end at the same point however it does not matter where you start on the loop.

The current direction must be assumed. The assumed current creates a voltage across each resistor and fixes the position of the positive and minute signs so that the passive sign convention is obeyed. The assumed current direction and polarity of the voltage across each resistor must be in agreement with the passive sign convention for the analysis to work. 

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