Ok. So we're talking about electricity here, an obscure subject for some but an important one nonetheless.

For all intensive purposes, electricity (electric current) can be defined as the flow of charges (typically electrons) from one place to another with a capability of doing work. For an electric circuit to be present, there must be a closed path in which an electric current can travel from an energy source (positive terminal), to an element in the circuit, and back to the energy source (negative terminal). Conventionally, the direction of the current is considered to be the movement of positive charges from + to - when in reality, it is the movement of negatively charged electrons from - to +. The common elements of a circuit are a battery (energy source), wires, and loads (lights, resistors, etc.) that are arranged in a closed loop with no breaks or gaps.

A DC (Direct Current) circuit is one in which the current travels in one direction continuously (a constant flow of electrons). An AC (Alternating Current) circuit is one in which the current is continuously and rapidly changing directions (the electrons are moving back and forth).

**A Series Circuit:**

A series circuit is one in which the elements in the circuit (lights, in this example) are arranged in line with each other, from end to end. Take, for example, the circuit below:

In a series circuit, the current is the same along all points in the wire. This is due to the fact that there is only one path for electrons to take (like cars traveling along a one lane road; they cannot pass each other). The equivalent (total) resistance of the circuit equals the sum of all the individual resistances of all the elements in the circuit. Even though the current is the same at all points, the voltage (potential electrical difference) across two points in the circuit is not. The voltage drop across each individual element in the circuit equals the voltage drop across the entire circuit (the voltage drop of the energy source). Basically, the voltages of the batteries are distributed between the elements in the circuit. In this example, the total voltage of the circuit is 75V. Because the two lights have the same resistance, they both have a voltage of 37.5V. Note: If elements in a circuit have different resistances, the distribution of the voltage will not be equal.

**A Parallel Circuit:**

A parallel circuit is one in which the elements are connected in parallel, meaning that each have a direct connection to the energy source (the lead from the energy source is split into many paths that lead to the elements).

In a series circuit, the voltage drop across each "branch" equals the voltage drop of the total circuit (voltage drop of the energy source). Even thought there are multiple paths, the voltage in each path is the same because it has, in essence, a direct path to the energy source (battery). However, the current drawn by each branch varies with the the resistance of each branch. Furthermore, as can be derived from Kirchhoff's current law (Conservation of Charge), the total current of the circuit equals the sum of the currents through each branch. The equivalent resistance of the circuit can be found by taking the inverse of the sum of the inverses of each individual resistance (each new resistance added decreases the equivalent resistance).

**A Complex Circuit:**

A complex circuit is a combination of elements in series and elements in parallel into one circuit.

In a complex circuit, things become more complicated. To find the equivalent resistance you combine the resistances of individual components (parallel segments and series segments). For this example, the equivalent resistance would be found by adding the resistances of the two series lights and the resistance of the parallel segment (as described above). The total current would be found by dividing the voltage drop of the energy source by the equivalent resistance of the circuit. To find individual voltage drops and currents at specific points, look at each component as a single entity and incorporate it into the larger arrangement. In this example, the parallel segment can be considered in series with the two other lights. In general, in situations similar to the one pictured above, to find the voltages of series elements multiply the individual resistances by the total current. To find the voltage of the parallel branch, subtract the series voltages from the total voltage. Now, you can find the different currents in the individual branches of the parallel segment: divide the voltage of the parallel branch by each individual resistance.

When working with circuits, do not memorize a certain method that can be used in every situation. Circuits are like puzzles; they take thought to work through every situation.

Have Fun!!!

**Attributions:**

AC/DC Photo: Photo by Yannick Croissant - http://www.flickr.com/photos/yannick-croissant/3315343302/

Lightning Photo: Photo by Fort Photo - http://www.flickr.com/photos/70619288@N00/3638881022

Electric Circuit Pictures: Screen shots while working in PhET simulation: http://phet.colorado.edu/simulations/sims.php?sim=Circuit_Construction_Kit_DC_Only