## Intro to Circuit Analysis

An electrical circuit is a closed loop path through which current can flow. An electrical circuit can be made up of almost any materials (including humans if we’re not careful!), but practically speaking, they are typically comprised of electrical devices such as wires, batteries, resistors, and switches. Conventional current will flow through a complete closed-loop path (closed circuit) from high potential to low potential, therefore electrons actually flow in the opposite direction, from low potential to high potential. If there the path isn’t a closed loop (open circuit), no charge will flow. Electric circuits, which are three-dimensional constructs, are typically represented in two dimensions using diagrams known as circuit schematics. These schematics are simplified, standardized representations in which common circuit elements are represented with specific symbols, and wires connecting the elements in the circuit are represented by lines. Basic circuit schematic symbols are shown in the Physics Reference Table.

In order for current to flow through a circuit, you must have a source of potential difference. Typical sources of potential difference are voltaic cells, batteries (which are just two or more cells connected together), and power (voltage) supplies. We often times refer to voltaic cells as batteries in common terminology. In drawing a cell or battery on a circuit schematic, remember that the longer side of the symbol is the positive terminal. Electric circuits must form a complete conducting path in order for current to flow. In the example circuit shown below left, the circuit is incomplete because the switch is open, therefore no current will flow and the lamp will not light. In the circuit below right, however, the switch is closed, creating a closed loop path. Current will flow and the lamp will light up. Note that in the picture at right, conventional current will flow from positive to negative, creating a clockwise current path in the circuit. The actual electrons in the wire, however, are flowing in the opposite direction, or counter-clockwise.

##### Kirchhoff’s Laws

Kirchhoff’s Current Law (KCL), named after German physicist Gustav Kirchhoff, states that the sum of all current entering any point in a circuit has to equal the sum of all current leaving any point in a circuit. More simply, this is another way of looking at the law of conservation of charge.

Kirchhoff’s Voltage Law (KVL) states that the sum of all the potential drops in any closed loop of a circuit has to equal zero. More simply, KVL is a method of applying the law of conservation of energy to a circuit.

Question: A 3.0-ohm resistor and a 6.0-ohm resistor are connected in series in an operating electric circuit. If the current through the 3.0-ohm resistor is 4.0 amperes, what is the potential difference across the 6.0-ohm resistor? Answer: First, let’s draw a picture of the situation. If 4 amps of current is flowing through the 3-ohm resistor, then 4 amps of current must be flowing through the 6-ohm resistor according to Kirchhoff’s Current Law. If we know the current and the resistance, we can calculate the voltage drop across the 6-ohm resistor using Ohm’s Law:  