Many technicians waste quite a bit of time doing circuit analysis because they end up analyzing too much of the circuit. If an output (usually a voltage drop across a load resistance) is all you are looking for, then you do not have to be worried about the voltage drops across each resistance or current through each branch.

This article shows how to keep the DC circuit analysis simple. These evaluation steps assume a purely series-parallel resistive circuit.

1. Determine output variable - Decide exactly what you are trying to find. Is it the voltage drop over a certain resistor? Maybe it is the current going through a certain branch. It may even be the active resistance of a component.

2. Determine input variable - Is the input a current or voltage source. Remember that a current source will supply as much voltage as necessary to provide a constant current. A voltage source will supply as much current as necessary to provide a constant voltage.

So, with a current source, the current value never changes. With a voltage source, the voltage value does not change.

3. Simplify the circuit - Many DC circuits can seem overwhelming. The good thing is that after determining what the input and output variables are. Most independent source circuits can be simplified down to a basic series or parallel circuit.

Use the additive property of resistance to simplify the circuit as much as possible. All resistance in series can simply be added to create an equivalent resistance. To combine resistances in parallel (resistances that share two common nodes) use the following formula (R1=total resistance in one of the parallel branches, R2=total resistance in the other parallel branch).

(R1 X R2) / (R1 + R2) = the product of R1 and R2 divided by the sum of R1 and R2. This is the equivalent resistance between the two common nodes.

To keep this circuit analysis process basic, only do two parallel branches at a time.

There are many techniques used to simplify circuits, but most go beyond the scope of this article.

The point is to simplify the circuit down to one loop of series components or a basic parallel circuit with only two branches.

Note - Never alter the components that are on the branch of interest (the branch that the output variable is on).

4. Solve for Output - Use the different laws of electronics to solve for desired output.

Ohm's Law: V = I X R = the voltage drop across a resistance is equal to the value of that resistance times the current going through it.

Kirchhoff's Voltage Law (KVL): The sum of all voltages in a loop is 0. Account for the polarity of each component. Start at one point in a loop. Following the direction of current add all voltage drops until you get back to the point where you started. If the current enters a positive pole, the voltage is positive. If the current enters a negative pole, the voltage is negative.

Kirchhoff's Current Law (KCL): The sum of all currents entering and leaving a node or enclosed area of a circuit equals 0. If the current is entering, it is positive. If the current is leaving, it is negative. This also means that the current entering a node or enclosed area equals the current leaving that node or enclosed area.

Other useful concepts and equations for step 4:

Current Division: Consider a parallel resistive circuit (simplified down to just two branches) with a known current source (Is). The respective branch resistances are R1 and R2. To find the current going through R1 simply the value of the current source by the resistance value of R2 and divide that product by the sum of the resistances... Current through R1 = (Is X R2) / (R1 + R2).

Voltage Division: Consider a series circuit that has more than one resistive component and a known voltage source. The voltage drop across one of the resistors is the product of the voltage source (Vs) and the resistor of interest divided by the sum of all resistance in the loop.

Ex... There is a series circuit with three resistances (R1, R2, and R3). We want to find the voltage drop across R3. Voltage across R3 = (Vs X R3) / (R1 + R2 + R3).

There are many other things that will need to be performing DC circuit analysis on more complex circuits.

I hope this article on DC circuit analysis has helped to clarify the procedure for analyzing series-parallel circuits.