**Ideal Independent Voltage Source: **One of the key circuit elements we will encounter this term is the ideal independent voltage source. One or more of the characterisitcs of an ideal independent voltage source may surprise you. It is important to remember however, that we are considering the source to be *ideal*. No element is truly ideal; we simply assume that we are considering situations in which the ideal model is sufficiently accurate. The symbol for a generic ideal independent voltage source is shown below in Figure 1.

An *ideal independent voltage source * provides a specified voltage difference regardless of the circuit to which it is connected. That is, the voltage difference across the source is independent of the current that may be in the source. Consider Figure 1 which shows an ideal 7.5 V independent voltage source connected to a hypothetical circuit.

The node at the higher potential side of the voltage source is labeled 'A' and that at the lower potential end, 'B'. Regardless of what the voltage source is connected to, node A will always be higher in potential than node B by 7.5V. The circuit to which it is connected may draw 1 A of current, 10 A of current, zero current or it may even be such that the direction of current will be opposite that suggested in Figure 1. Regardless of the case, node A will be higher than node B by 7.5V. It is important to understand that there is zero internal resistance in an ideal independent voltage source.

In the next tab, we will examine the current-voltage characteristic of an ideal independent voltage source to better understand the role of the current that exists along an ideal independent voltage source. Before moving on however, click on the circuit of Figure 2 to toggle between the possible cases of the current along the voltage source. In all cases shown in Figure 2, the current is assumed positive in the direction of the arrow.

It can be helpful to think about the currrent-voltage (I-V) characteristic of an ideal independent voltage source. An I-V characteristic is a plot of the current associated with an element as a function of the voltage drop across the element. An ideal independent voltage source provides a specified voltage drop regardless of the amount of current in the voltage source. Thus, as shown in Figure 3, the I-V characteristic of an independent voltage source is a vertical line that cuts through the voltage axis at a value equal to V_{s}. The I-V characteristic tells us that when the source is placed in a circuit, the actual current in the voltage source will depend on the circuit as a whole and that we are only guaranteed that the potential difference across the voltage source is V_{s}.

An important point to be made with regard to Figure 3 is that the direction of current is assumed to be from higher to lower potential along the voltage source, in accord with the passive convention. When we sketch an I-V characteristic we must be clear about the assumed polarity of voltage and direction of current. Why? Consider the case of Figure 4, the I-V characteritic of a 5V source.

On the left of the figure we see the circuit symbol of a 5V ideal independent voltage source in which the current is drawn in accord with the passive convention. The I-V diagram on the right of the figure is the expected vertical line cutting through the voltage axis at 5V. If the current in the voltage source is positive, that is through the voltage source from higher to lower potential, the source is absorbing energy. If on the other hand, the current is directed from lower to higher potential through the source, the current is negative as drawn and we are considering the fourth quadrant of the I-V characteritic. In this case, the source is supplying energy to the circuit. Can a voltage source absorb energy? Yes, perhaps it represents a battery being charged for example. To visualize the absorbing versus supplying concept more clearly, click on various sections of the line in Figure 4 to see whether the voltage source provides or absorbs energy. If you click on the point V = 5V, I = 0A, you should see that under this condition, the source neither provides nor supplies power.

The important point to be made is that an ideal independent voltage source will provide a specified potential difference across its terminals regardless of the current through the source. This point will be made clear when we consider a couple of examples. In the examples tab, we look at the "operating point" of a 3V ideal independent source when placed in two different circuits.

Consider the I-V characteristic of a 3 volt ideal independent voltage source as suggested in Figure 5.

At the top left of the figure we see the voltage source's circuit symbol and the assumed direction of current for constructing the I-V characteristic that is shown at the right of the figure. As we know, the I-V characteristic of such an element is a vertical line with V = 3V. When we place the 3V source in a circuit, we must examine the entire circuit to determine the value and direction of the current source. As an example, consider the circuit at the lower left of the figure. Here, the 3V source is connected in a simple circuit with a 1.5 ohm resistor. Ohm's law tells us that the magnitude of the current will be (3V)/(1.5ohms) = 2A. But what is the direction? We know that resistors are passive elements and thus current is directed through them from high to low potential. As the top of the resistor is 3V higher than its bottom, current is directed clockwise in the circuit. Therefore, current is opposite our assumed direction suggested in the figure. This reveals that I = -2A. Now click on the I-V characteristic to notice the "operating point" at coordinate pair (3,-2). Thus, the voltage source is operating in the fourth quandrant. Look back to the previous tab and you will see that this indicates the voltage source is supplying energy. This is to be expected as it is the only source in the circuit with the other element being a simple resistor.

In the next example, we will once again consider the same 3V source, but placed in a different circuit. This second circuit is shown in Figure 6 and is a bit more involved. Notice that the I-V characteristic of the 3V source is the same as that shown in Figure 5, but since the 3V source is connected to the 1.5 ohm resistor and a 7V source as suggested at the lower left of the Figure 6, we expect its operating point to be different. You are to work towards an understanding of the circuit by answering the questions that follow.

As was mentioned in the introduction, there is no such thing as an ideal independent voltage source. It is only a model that is often helpful and sufficiently accurate for basic calculations. In the lab you will often use a simple programmable DC power supply. You will set the voltage to a certain value and expect the power supply to provide precisely that value to your circuit. Is that an acceptable expectation? Assuming a well-designed supply, the voltage source should provide very close to that voltage as long as the accompanying current required of the circuit at that voltage falls within the supply's specification.

For example, consider a power supply with a 30V and 3A limit. What does this mean? This means that the supply can establish voltage differences up to 30V as long as the instrument is asked to handle no more than 3A. If the circuit is such that it demands more than 3A, the channel will enter a "constant current" mode in which the current is pegged at 3A and the voltage is such that only 3A is demanded.

Imagine that a 30V 1A DC supply is connected to a 12 ohm resistor and that the supply and the resistor form a complete circuit. The user sets the voltage to 22V.

*What value of current is expected in the circuit and what is the expected voltage across the resistor?*