How to Find Voltage Drop in a Series Parallel Circuit

Note any values you know on the circuit diagram. For example, if you know the values of the resistors in the diagram, write each resistor's value next to it. If you know how much current is flowing across an element, draw an arrow next to that element in the direction of the current flow and note the current.

On the circuit diagram, use a colored pencil to trace one closed loop. Start at one point and go around counterclockwise or clockwise until you return to the same point. If there is more than one loop, use a different colored pencil to trace each one.

Mark nodes where two or more wires connect with dots (use a regular pencil).

Draw arrows representing the currents entering and leaving each node. Denote unknown current magnitudes as i1, i2, i3 and so on.

Write the voltage drop across each element symbolically, in terms of current across that element (whether you know the current magnitude or not) and that element's resistance, capacitance or inductance. If you do not know the resistance, capacitance or inductance of an element, denote it with R1, C1 or L1 (R2, C2, L2 and so on, depending on how many unknown quantities you have).

Start at one point on the first loop. Move around the loop and write down the symbolic representation of the voltage drop across each element on that loop until you get back to your starting point. Write an equation setting the sum of all those voltage drops to zero. If you go across a battery or other potential source, remember to express a rise in voltage as a negative voltage drop.

Repeat this process for all the loops of the circuit. You will end up with one equation for each loop. If the circuit has two loops, you will have two equations; three loops with have three equations and so on.

For each circuit node, write an equation with the currents entering that node on one side, and the currents leaving that node on the other side. You will have one equation for each node.

Solve the resulting system of equations for the unknown quantities. This can be done by hand if there are a relatively small number of equations and unknowns; otherwise, it may be easier to use a computer.

Once you have values for all unknown quantities, plug them back into the expressions you wrote for voltage drop across each element, and compute the voltage drops. Now you have a complete picture of voltage drops in the circuit.