Voltage
Introduction: This article focuses on the purpose of voltage and how it applies within circuit theory.
The Essentials
An electrical phenomena we are interested in is known as voltage. Voltage can be seen as the force driving the electrons through a given circuit. It is also described as a potential difference.
Voltage, in technical terms, is described with this equation:
where
\( v_{ab} \) = the voltage in volts between points a and b
w = the energy in joules
q = the charge in coulombs
This describes voltage as the electric force. This force moving electrons is understood as the change of energy over charge.
Example
One characteristic of voltage is its polarity. The plus (+) and minus (-) sign are used to define the direction of the voltage. The force goes from negative (-) to positive (+).
Figure 1 contains an example of the polarity of an circuit element. This image contains a circuit element with a voltage polarity across it, positive at the top and negative at the bottom. This polarity is labeled as \( v_{ab} \)
Figure 1: Polarity of voltage \( v_{ab} \)
In some circuits, we may be given different representations of a given voltage. Figure 2 demonstrates one representation. This figure contains two different examples of polarity across an element. The first element contains a positive terminal at the top and negative at the bottom. The second element is vice versa, that being negative at the top and positive at the bottom. The first element is labeled to have a voltage of 9 V comparing the positive to the negative. The second element is labeled to have a voltage of -9 V since we are comparing negative to positive. For both elements, the top node is labeled as a, and the bottom is labeled as b.
Figure 2: Swapping polarities of voltage \( v_{ab} \)
With the previous explanation in mind, we can see that the voltage \( v_{ab} \) in example (a) of Figure 2 is 9 Volts. However, in example (b), the polarity changes, now making \( v_{ab} \) is -9 Volts.
With this in mind, we can make the following conclusion in Equation 2.
Practice
Figure 3: Problem 1 \& 2
Problem 1.) Using Figure 3., determine the voltage \( v_{ab} \). Figure 3. contains an image of a circuit element with positive terminal at the top and negative at the bottom. The top node is a and the bottom node is b. The voltage labeled across the element is 12 volts.
Problem 2.) Using Figure 3., determine the voltage \( v_{ba} \).
Solutions:
Problem 1 Solution.) \( v_{ab} \) = 12 V. This is because we are given the value of the voltage across the two nodes of the element and the reference points (in this case, measuring point a with respect to b).
Problem 2 Solution.) \( v_{ba} \) = -12 V. This is the same reason as the previous problem, but now we are curious of the voltage of b with respect to a. This reference point is opposite of the previous problem, and since it is opposite, we remember equation 2 listed above and conclude the voltage \( v_{ba} \) is indeed -12 V.