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This module is part of the collection, A First Course in Electrical and Computer Engineering . The LaTeX source files for this collection were created using an optical character recognition technology, and because of this process there may be more errors than usual. Please contact us if you discover any errors.

In this section we use the linear algebra we have developed to find the voltages and currents in a simple electrical circuit, such as the one shownin Figure 1 . There are many reasons why this might be necessary; in this example we need to know the current flowing through the lamp to tell whetheror not it will glow. Too little current will have no visible effect; too much current will cause the lamp to burn out. We will apply a few physical lawsrelating the voltages and currents in a circuit, turn these laws into systems of linear equations, and solve the equations for the voltages and currents.

The diagram is essentially a rectangle. In the middle of the left side of the rectangle is a circle labeled on the left with a 5 and on the top right and bottom left with a + and - respecitively. On the left side of the top there is a resistor labeled 50. In the middle there of the top side there is a point with a line that bisects the rectangle this line also has a resistor that is labeled 300. On the right side of the top there is a resistor labeled 100. On the right side there is a resistor labeled 2 and to the right of that is the word (lamp). The diagram is essentially a rectangle. In the middle of the left side of the rectangle is a circle labeled on the left with a 5 and on the top right and bottom left with a + and - respecitively. On the left side of the top there is a resistor labeled 50. In the middle there of the top side there is a point with a line that bisects the rectangle this line also has a resistor that is labeled 300. On the right side of the top there is a resistor labeled 100. On the right side there is a resistor labeled 2 and to the right of that is the word (lamp).
A Simple Electrical Circuit

Current, Voltage, and Resistance. We will use three physical quantities in our analysis of electrical circuits: current, voltage, and resistance. Current is the flow of electrical charge from one place to another. Electrons flowing through a wire or through some other electronic device comprise acurrent. Voltage is a difference in electric potential that makes electrons flow. Voltage is sometimes called electromotive force because it is like a “force” that moves electrons. Resistance is a property of the device through which the electron current flows. The lower the resistance of a device, the moreeasily current can flow through the device.

The analogy of water flowing through pipes can help you develop intuition about electrical circuits. In this analogy, electrical current corresponds to the flow rate of water. Voltage corresponds to the pressure that forces the water to flow, and resistance is the friction of flow. A small pipe would impede the flow of water more than would a large pipe, so the small pipe would correspond to a higher resistance. While this analogy can be helpful, keep in mind that electricity is not water. All analogies break down at some point.

We measure electrical current in amperes . The standard symbol for current is i , and the direction of positive flow is indicated by an arrow on the circuit diagram. The arrow is for reference only; if the true current is in the opposite direction, we get negative values for i . Because electrons are negatively charged, current is defined as flowing in the opposite direction as electron motion. But to reduce confusion, you should learn to think in terms of current rather than electron motion.

A point in a circuit where several devices are connected together is called a node . The conservation law for current says that “what flows in must flow out of a node,” a principle known as Kirchhoff ' s current law . Kirchhoff's current law states that the sum of all currents leaving a node is zero . In this law, a current entering the node is considered to be a negative current leaving the node.

Voltage is measured in volts and is usually written as v (or e ). Since voltage is a difference in potential between two points (nodes), we can show it on a circuit diagram with a + a n d a –sign to indicate which two nodes we are comparing and which one of the nodes is considered negative. As with current, the markings are for reference only and we may end up with a negative value of v .

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Source:  OpenStax, A first course in electrical and computer engineering. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col10685/1.2
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