Electric Circuit Analysis/Passive Sign Convention

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Introduction
This is the first of eight lessons in Electric Circuit Analysis. This course is a pre-requisite course to most Level 2 courses in this school. As such it is imperative that a student gains insight into the methods and theory introduced and explained in this course.

There are plenty of worked examples and an exercise at the end of the lesson. Work through the exercise on your own, and only then can you compare your results with the solutions given on a linked Sub-page.

Lesson Preview
This Lesson is about Passive sign convention. This Lesson introduces a student to Circuit Elements which will be encountered in Electric Circuit Analysis. The student/User is expected to understand the following at the end of the lesson.
 * Active Circuit Elements
 * Passive Circuit Elements
 * Passive Sign Convention
 * Guidelines for Passive sign Convention

Remember that Open Learning is all about you. You can set your own pace in this course and you will be helped to evaluate your self along the way.


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Part 1: Electric Circuit
An electric circuit is a connection of circuit elements (Voltage/Current sources, Resistors, Inductors, Capacitors etc.) such that there is some power supplied and dissipated. This means that if you connect a resistor to a battery using conductive wires, then you have created an electrical circuit.

Active Circuit Elements:
All circuit elements that are capable of supplying electric power to a circuit or to an aspect of the circuit for an indefinitely long time are called active circuit elements. Batteries and generators are examples of active circuit elements. Figure 1.1 shows circuit symbols used to depict a Voltage Source (an ideal battery) and a Current Source. Notice that the circuit elements show a polarity&mdash;either a reference label for the voltage or an arrow giving a reference direction for the current or both. There is also a mathematical equation associated with each circuit element. For a voltage source, V = 5 volts (or any constant) is an example of such an equation. For a current source, I = 2 amperes (or any constant) is another example.

Transistors, vacuum tubes (valves), and many other circuit elements are also active elements even though they cannot supply electrical power to the entire circuit for an indefinitely long time. These components take electrical power from one part of the circuit (often called a power supply) and deliver the power to another part of the circuit (often by way of amplifying a signal) and can do this for an indefinitely long time.

Note that an element is active if it is capable of the above. Even if it is not delivering power to a particular circuit (or an aspect of a particular circuit) it might still be an active circuit element.

Passive Circuit Elements:
Philosophically speaking, any circuit element that is not active is passive. This means that passive circuit elements absorb or dissipate electric power in the long term. In the short term they may store some electric power and then return that power back to the circuit at a later time. Even if a circuit element is 100% efficient in this storage and return process, it is passive because it cannot deliver power over an indefinitely long time. (Of course nothing more than 100% efficient exists. Active circuit elements have a source of energy to draw on, such as the chemicals in a battery.  Passive elements do not.)  A resistor is a good example of a passive circuit element. The following picture shows circuit symbols used to depict a Resistor. The symbol shown in Figure 1.2 for a resistor is generally preferred in Europe and some other parts of the world and will be used throughout this course. The symbol shown in Figure 1.3 is generally (but not always) used in the Americas.

Elsewhere in this wiki, a "circuit element" may be called a "component." The word "component" has similar meaning, but is not so strictly defined. The phrase "circuit element" is defined to mean the association of three things: 1.) An electrical device with a defined number of connections having polarity reference labels (+ and - marks, visible or implied, or current arrows, visible or implied.) 2.)  A mathematical relationship between voltages and currents at the defined terminals. 3.) An irreducible nature&mdash;the device cannot be manufactured as a connection of simpler circuit elements.

Please note that capacitors and inductors are beyond the scope of this course as they introduce complex current and voltage relationships.


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Part 2: Passive Sign Convention
The concept of passive sign convention comes directly from the definition of voltage.

Voltage is a difference of charge between two places in space. Not an absolute quality. You could think of it in terms of depth and height.

Something has an elevation or height only with respect to something else such as sea level. Likewise depth, something is only deep compared to some level, again such as sea level.

There is one difference between depth and height. We consider height to be positive and depth to be negative. One of the reasons why we do this is because we usually deal more with height than depth, and we wish to minimize the amount of subtraction that we perform.

The passive sign convention is the same concept. It is an algorithm to decide what is adding potential energy to the system and what is taking it away.

Here are some basic ground rules:


 * All resistors are either positive or negative uniformly. Which means that if you consider one resistor to be positive (which is the common case) then all the resistors are positive.
 * At least one source is the opposite sign of the resistors. If only one is present then that is the one.
 * Always start by making your loop.

Why do we use this Passive sign convention?
One of the most important ideas of an electric circuit is that there is a source of power and a dissipator of power. As circuit connections become more intricate this basic idea becomes more blurred. In some cases there are more than one power supply at different circuit locations, such that simple addition of their power magnitudes is not possible. We need to know which direction power supply and consumption is. The next examples will illustrate this.


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Part 3
Points A and B are physical end points of an element. By convention A (+) has a higher potential than B (-) by amount V. If V is negative, then B has higher potential than A, but the signs for polarity remain unchanged. The current I enters point A and leaves point B. If I is negative, then current is entering point B and exiting point A.


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Explanation of Part 3
An electric charge Q at point A moves from a higher potential to a lower potential (i.e. from point A to point B). Since the charge is now at a lower potential, the charge has lost potential energy. This is called a resistor. If the charge moves from B to A, it gains potential energy. This is called a source.

If we keep A and B as the (+) and (-) terminals, then there are four possible combinations. The two cases (-V, -I) and (+V, +I) are ones where the element acts as a resistor, using up energy. The two cases (-V, +I) and (+V, -I) are ones where the element acts as a source, supplying energy.

If we flip A to be (-) and B to be (+) then we have effectively rotated the element by 180 degrees. All of the above cases still hold true.

Being comfortable with the convention and being able to quickly visualize different combinations of +/- I or +/- V from either terminal A or B will help in using the circuit solving methods of Mesh and Nodal Analysis.

The following examples are related to the lesson. The answers to the exercise questions are given as a link to a sub page. Attempt the problems before viewing the answers.


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Example 1.1
Figure 1.5 shows an element with the following parameters. $$V_R=9Volts$$, $$I_R=3A$$ Find $$P_{Total}$$ and Determine if this element is a resistor. Is it supplying power or dissipating it?

Solution:

$$\begin{matrix}\ P_{Total}&=&V_R \times I_R \\ \ \\ \ &=& 9V \times 3A \\ \ \\ \ & = & 27Watts \end{matrix}$$.

Since power is positive, this is a resistor which absorbs power.


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Example 1.2
Figure 1.6 shows a simple element with the following parameters: $$V_R=-6Volts$$, $$I_R=3A$$ Find $$P_{Total}$$ and determine if this is a resistor or a source and if it is supplying power or dissipating it.

Solution:

$$\begin{matrix}\ P_{Total}&=&V_R \times I_R \\ \ \\ \ &=& -6V \times 3A \\ \ \\ \ & = & -18Watts \end{matrix}$$.

Since power is negative, this is a source which supplies power.


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Example 1.3
Figure 1.7 shows an element with the following parameters. $$V_R=-6Volts$$, $$I_R=-3A$$ Find $$P_{Total}$$ and determine if this is a resistor or a source.

Solution:

$$\begin{matrix}\ P_{Total}&=&V_R \times I_R \\ \ \\ \ &=& -6V \times -3A \\ \ \\ \ & = & 18Watts \end{matrix}$$.

Since power is negative this is a source, and it is supplying power.

The simplest method to solving this problem is to redraw it with the top of the terminal being (+) and the bottom being (-). As the problem is presented, the voltage is -6 V between the terminals and the current is -3 A coming out of the positive terminal (+). By switching the poles, we also flip the direction of the current and the voltage. As a result, we now have a voltage of 6 V and a current of 3 A. Since the voltage difference and the current flow are in the same direction, this component must be a resistor like in Example 1.1.

It is important to remember that switching the poles in this way does not change the physical reality of what is happening. Regardless of which pole is (+) or (-), the top terminal has greater potential than the bottom terminal, and current is flowing from the top to the bottom (see Charge Conjugation Symmetry).

Now, try the exercises to test these concepts.


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Exercises

 * 1) Use Figure 1.5: Given current is 4 A and the voltage across the element is 4 V, how much power is being produced or consumed?
 * 2) Use Figure 1.5: Given current is 1.5 milli-Amps (mA) and the voltage across the element is -1.5 V, how much power is being produced or consumed?
 * 3) Use Figure 1.5: Given current is 15 A and the voltage across the element is 15 V, how much power is being produced or consumed?
 * 4) Use Figure 1.5: Given current is -20 mA and the voltage across the element is -1.5 V, how much power is being produced or consumed?


 * Answers to Exercise 1



Completion list
Once you finish your Exercises you can post your score here! To post your score, just e-mail your course coordinator your name and score *@undefined.


 * Ozzimotosan -- 75% & Corrected
 * Doldham -- 75% & Corrected
 * Jacob -- 100%, fixed the page.
 * Drew -- 100%,


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