# Basic Circuit Concepts:

## Introduction

Electrical circuits provide a way to control electricity. Electricity is the flow of charge (typically electrons) or the accumulation of charge (although in basic circuit theory we assume that charge does not accumulate—the net flow of charge into a device is equal to the net flow of charge out of the device). When you first start to think about electrical circuits it can be helpful to think of them as being analogous to hydrological systems where water flows through pipes. (There are various ways in which this analogy ultimately breaks down, but the analogy is useful nonetheless.) When building a hydrological system, it is important to keep track of the flow rate and pressure of the water. We describe electrical circuits similarly: current is the rate at which charge flows past a point, while the voltage is effectively like an electrical “pressure.” Voltage is always measured between two points and indicates the force “pushing” charges to flow from one point to another. The purpose of an electrical circuit is to accomplish some meaningful task such as generating light or heat, exerting a force (which may, for example, cause a motor's shaft to turn), or even sensing the physical surrounding with devices whose properties vary with changes in the surroundings (such as a temperature probe). Electricity provides the means to transport energy from a source to a load. The source of energy might be a battery while the load is a light-emitting diode (LED) and the desired task is to cause the LED to illuminate. If too much charge flows through a circuit, the circuit or its components can be damaged. To prevent this, voltage and/or current can be limited through the use of components known as resistors. As their name implies, resistors are characterized by the property of resistance, which is like a form of electrical friction. Resistors dissipate energy as heat.

The remainder of this page provides a very brief overview of current, voltage, and resistance and how they are related. To obtain further details, please click on the boxes that are given below on the right side of the page.

## Resistance and Resistors

• Water Analogy: Physical obstruction such as a wire mesh or bottleneck.
• Units (Symbol): Ohms (Ω, i.e., the Greek letter Omega).
• Equation Variable: $R$

Brief Description: Electrical resistance is a measure of how easily charge can move through circuit elements. The greater the resistance, the more difficult it is for charge to flow. Although all materials have some resistance, wires (and metals) generally have very little resistance and are often approximated as having no resistance (a resistance of zero). Thus the assumption is that wires provide a resistance-free path to deliver energy from one point to another. On the other hand, circuit components known as resistors are designed to offer a specified resistance to the flow of charge.

Resistors are often color coded to indicate their amount of resistance. There is more information regarding this topic available via the “Practical Resistors” link on the right that shows how you can determine resistance from the colors on a resistor.

## Current

• Water Analogy: Flow rate.
• Unit (Symbol): Amperes (A).
• Equation Variable: $I$ or $i$.

Brief Description: Current is the measure of how much electrical charge flows past a point in a given time. Current is measured in Amperes, often called simply amps. One Ampere corresponds to the flow of $6.241 \times 10^{18}$ electrons per second. (Although it is peripheral to our particular interests, electrons have negative charge, so if electrons are flowing in one direction, we say the direction of “positive” current flow is actually in the other direction. However (and fortunately), one is almost never concerned with the “sign” of the charge carrying the current. Insofar as circuit analysis goes, we are interested in voltages and currents and the underlying charge carrier is not of interest.)

## Voltage

• Water Analogy: Pressure.
• Unit (Symbol): Volts (V).
• Equation Variable: $V$ or $v$.

Brief Description: Voltage measures the relative difference in electric potential energy. This means that it is a comparison of the energy levels at two separate points. This difference is often called the voltage drop. If you image two pools of water that are at different heights and a pipe that links them, because of gravity, there is a difference in the potential energy in the water in the two pools. The water in the higher pool has greater potential energy. This water is willing to give up this stored energy by flowing to the lower pool. The pressure in the pipe that joins these two pools (caused by the difference in potential energy) is analogous to a voltage.

It is important to remember that voltage is always measured relative to two selected points. In practice, we usually designate a single point of reference in a circuit to serve as the common reference point for all voltage measurements. We typically refer to this point as ground. The difference in voltage between ground and itself is, of course, zero. So ground is assigned a voltage of 0V. All other voltages that we specify for a circuit are the difference in electrical potential between that point and ground.

However, one should keep in mind that the ground (0V) we designate for a circuit is not on an absolute scale. Yes, there is a point in our circuits that we define as ground, but there is also a concept of earth ground. Essentially, earth ground assumes that voltage measurements are relative to a large metal rod driven into the earth. Since measuring voltages relative to earth ground is rather inconvenient, we instead define a circuit ground or signal ground that is convenient to our circuit. (There may or may not be a non-zero voltage between our circuit ground and earth ground, but if there isn't a path for charge to flow from our circuit to a large metal rod driven into the earth, we really aren't concerned about this voltage.)

Because voltage is a measure of the difference in potential energy between two points, it can be either positive or negative. So, for example, if the voltage measured from point A to B is positive, that simply means that point A is at a lower potential than point B and (positive) charge will want to flow from point B to A. Conversely, if the voltage measured from point A to B is negative, that means that point A is at a higher potential than point B and (positive) charge will want to flow from point A to B. Voltmeters (which measure voltage) typically have two probes labeled positive and negative. If the negative probe is connected to the point with the lower potential and the positive probe is connected to the point with the higher potential, the voltmeter will display a positive voltage. If the probes are reversed, the voltmeter will display the same magnitude of voltage, but now it will be negative. (As an aside, the power delivered to your home comes in the form of an “alternating current” signal. In this case the two outlets in a wall socket alternate back and forth between which is at the higher potential.)

## Ohm's Law and Current-Voltage Relationships

The three basic electrical properties mentioned above are related to each other by Ohm's Law. If we continue to use the water analogy to explain the relationship between voltage, resistance, and current; voltage (VOLT) being the water tries to push charge (AMP) along a path of a hose, while resistance (OHM) is the thing that inhibits the charge's movement (the wall of the hose). Ohm's Law provides the mathematical relationship between the quantities. It states that voltage is equal to current times resistance, or $V = I\times R$. Or, solving for current, we can write $I = V/R$. This tells us that if the voltage is held fixed while the resistance is increased (so that we are dividing by a larger number), the current will decrease. Conversely, if the voltage is held fixed while the resistance is decreased, the current will increase.

For the electrical components known as resistors, the resistance $R$ is fixed. Thus, the voltage varies linearly with changes in the current $I$. By “linearly,” we mean that if you plot the voltage versus the current for a resistor, the plot is a straight line. A plot of voltage versus current is known as a VI plot or VI curve. However, it is often more useful to plot the current versus the voltage and these plots are known as IV curves. In general, the relationship between current and voltage is known as the IV relationship.

Figures 1 and 2 depict the IV relationship for a “large” and “small” resistor, respectively. When the resistance is large, as in Fig. 1, the slope of the line is relatively shallow because the voltage is being divided by a large value and thus changes in the voltage do not have a large effect on the current (recall that $I=V/R$). When the resistance is small, as in Fig. 2, the slope of the line is relatively steep because the voltage is being divided by a small value (you can think of this as the voltage being multiplied by a relatively large value) and thus changes in the voltage do have a relatively large effect on the current.

Although current and voltage are linearly related in a resistor, many electrical components have nonlinear IV relationships. For example, the IV relationship of a component known as a diode is nonlinear, as shown in Fig. 3. With this particular nonlinear relationship, a small increase in voltage can cause a large increase in current (as is the case toward the right-hand side of the IV curve). On the other hand, if the voltage is negative, changes in voltage have very little effect on current. Ideally, a diode allows current to flow freely in one direction (when the voltage is positive) and does not allow current to flow in the opposite direction.