• The voltage drop V across a resistor is the negative of change in voltage DV across a resistor. This definition allows us to use a single variable V in a circuit equation that is positive.

Loop emf Drops and Gains:

While going around a loop, if you traverse a battery whose polarity is in the opposite direction you are moving then the voltage of the battery is negative - it is a loss not a gain.

Loop Resistor Drops and Gains:

While going around a loop, if your assumed direction for the current flow is opposite the direction you are moving around the loop, then the voltage drop across a resistor is a voltage gain.

Loop Capacitor Drops and Gains:

While going around a loop, if you traverse a capacitor whose polarity is in the opposite direction you are moving then the voltage of the capacitor is a voltage gain - it acts like a battery supplying voltage.

Applying Kirchhoff's Rules:

• Determine which branches of the circuit have a different current flowing through them and attach labels to the currents flowing in each branch. Components in series will have the same current so there is no need to use more than one label in a series branch.
  
  
• Assume a direction for the current flow in each branch of a circuit. You do not have to know which way the current is actually flowing for your solution to be correct. If you choose the wrong direction and do the problem correctly, you will get a negative answer of the current. Meaning that the current is flowing opposite to your initial assumption.
  
  
• Apply Kirchhoff' s Current Rule to the circuit junctions. This means write down the equation(s) that relate the currents flowing into that junction with the currents out of that junction.
  
  
• Choose a closed loop in the circuit and pick a direction around the loop. Your choice is arbitrary in that you should get a correct solution no matter which direction you pick for the loop - either clockwise or counterclockwise. It will make the solution less confusing if you can chose the loop in the same direction as the current is flowing. However, it is often not possible to do this for every section of the loop. See the voltage drops and gains above for more details on each component.
  
  
• Apply Kirchhoff's Voltage Rule to the loop. This means pick a starting point in a loop and go around it and write down the voltage gains and drops until you return to your starting point. It some instances a battery can be a voltage drop rather than a gain if its polarity is opposite loop direction you have chosen.
  
  
• If you have several variables to determine, you may need to choose additional loops and repeat the above. In the end you need to generate a set simultaneous linear equations to solve, one for each unknown variable that you will have to solve.