Common Misconception 2: Ideal Voltage Sources In Series and Parallel
Common Misconception 2 :
Ideal Voltage Sources In Series and Parallel
Almost all the circuits you will analyze in electric circuits courses contain one or more voltage sources and so know how to properly account for them is vital. There are several common misconceptions that a beginning student may exhibit when dealing with these common elements. This reading exercise briefly reviews the model of an ideal independent voltage source and then explores how one should interpret series and series and in parallel combinations of such sources.
To begin, let’s consider Figure 1 that depicts three circuits, each containing a single resistor and one or more ideal independent voltage sources.
Figure 1: Three circuits with a single resistor and one or more ideal independent voltage sources. All resistors are identical; all voltage sources are identical.
Before we proceed any further, please answer the following question. Assuming all sources are identical, and that all resistor are identical, select the option that correctly orders the circuits in terms of which provides the most power to its resistor.
The key properties of an ideal independent voltage source are apparent in its name. It is a source of voltage, or more formally, a source of potential difference and this potential difference is independent of the circuit to which it is connected. For example, consider the circuit of Figure 2 in which a 9V source is connected to an arbitrary circuit.
Figure 2: A 9V ideal independent voltage source connected to a generic circuit. The circuit to which the voltage source is connected could contain any type and any number of other circuit elements.
The two key properties to remember regarding the ideal independent source of Figure 2 are:
- Regardless of the circuit to which it is connected, the potential at node A will be 9V higher than that at node B. In other words, the source guarantees that the potential difference from node A to node B is 9V as its potential difference is independent of everything else in the circuit to which it is connected. We may write VAB = 9V.
- The current associated with the voltage source does depend on the circuit to which it is connected. The current might be directed through the voltage source from node B to node A, the current might might be directed through the voltage source from node A to node B, or there may be cases in which there is no current in the voltage source. Click on Figure 2 to see these three cases.
Now that we have highlighted these two key concepts underlying the model of an ideal independent voltage source, let’s go to the next tab and think again about the three circuits from the introduction tab.
Consider Figure 3 which is that from the introduction tab but now with nodes labeled A through G.
Figure 3: Three circuits with a single resistor and one or more ideal independent voltage sources. All resistors are identical; all voltage sources are identical. The nodes of each circuit have been labeled.
Let's attempt to apply what we reviewed in the previous tab: Select all the following options that are correct regarding the three circuits of Figure 3.
In the previous tab, we looked at three circuits and determined the voltage drop across the single resistor in each circuit. What if we want to know which of the three circuits delivers the most power to its resistor? This was the question posed in the introduction tab. To answer this question, let's first recall the fundamental equation that relates power to the potential difference and current associated with an element.
Figure 4: Generic circuit elements -- the left element is dissipating (or storing) energy and the right element is providing energy. In both cases the power is given by the product of V and I. That is, P=VI.
Let's say that instead of the generic elements of Figure 4, we are dealing with a resistor. Which case of Figure 4, the left or the right would pertain to a resistor?
While the power of any element is given by P=VI, when we are considering a resistor, there are two other forms, one of which may be particularly convenient depending upon the case. Recall that Ohm's Law states: V=IR. Using Ohm's Law we may write the power associated with a resistor as follows:
Perhaps the third representation, P = V2/R, is the most helpful here. Since the three circuits we have been considering have a single resistor of the same value, determining which circuit provides the most power to the resistor comes down to determining which resistor has the largest potential difference across its terminals. Proceed to the "Your Turn" tab to try a similiar problem as given in the introduction tab as well as to confront a new situation that requires you to more deeply consider the model of an ideal voltage source.
Just as we did in the introduction tab, let’s consider three circuits, each containing a single resistor and one of more ideal independent voltage sources of equal value.
Figure 5: Three circuits with a single resistor and one or more ideal independent voltage sources. All resistors are identical; all voltage sources are identical.
Select all the following options that are correct regarding the three circuits of Figure 5.