Ideal Independent Voltage and Current Sources

Ideal Independent Voltage and Current Sources

Introduction

Circuit elements are commonly categorized as either passive or active. A circuit element is passive if the total amount of energy it delivers to the rest of the circuit (over all time) is non-positive. (Passive elements can temporarily deliver energy to a circuit, but only if the energy was previously stored in the passive element by the circuit.) An active circuit element has the ability to create and provide power to a circuit from mechanisms external to the circuit. Examples of active circuit elements are batteries (which create electrical energy from chemical processes) and generators (which create electrical energy from mechanical processes. A good example of this would be the spinning of a turbine).

There are a variety of types of active sources. They are broadly categorized as:

  1. Ideal independent sources
  2. Non-ideal independent sources
  3. Dependent sources

In this exercise we will talk about ideal independent sources. We will consider two basic types of sources: voltage sources and current sources. From a practical standpoint, we will only implement voltage sources for now —current sources can wait until later.

Ideal Independent Voltage Sources

An independent voltage source maintains a specified voltage across its terminals. The symbol used to indicate a voltage source delivering a voltage Vs(t) is shown in Fig. 1. As indicated in Fig. 1, the voltage supplied by the source can be time varying or constant (a constant voltage is a special case of a time varying voltage). An alternate symbol that is often used to denote a constant voltage source is shown in Fig. 2; however, we will generally use the symbol of Fig. 1 for both time-varying and constant voltages.

Figure 1. Independent Voltage Source.
Figure 2. Constant Voltage Source.

Please keep in mind that, for ideal independent voltage sources, we know exactly what the voltage difference is; it has to be the value shown next to the source symbol. We also know the polarity of the voltage—the “+” and “-” signs on the symbol tell us the polarity. However, we know nothing about the current through the source! This tends to be confusing at times, and can be the source of many silly mistakes. Even the current direction is unknown1—anything we want to find out about current must be determined (if necessary) from an analysis of the overall circuit.

Ideal voltage sources provide a specified voltage regardless of the current flowing through the device. Ideal sources can, obviously, provide infinite power; all real sources will provide only limited power to the circuit. We will discuss approaches for modeling non-ideal sources in later projects.

Ideal Independent Current Sources

An ideal independent current source maintains a specified current. The circuit symbol for an ideal independent source is shown in Fig. 3. Note that the current value is listed next to the circuit symbol and that the direction of current flow in the source is provided on the source symbol—there is no need to assume a current direction2. The current supplied by the source can be time-varying or constant.

The current provided on the circuit symbol is maintained regardless of the voltage difference across the terminals. Even the voltage polarity is unknown and must be determined (if necessary) from an analysis of the overall circuit.

Figure 3. Independent current source.

Important Points

  • Ideal voltage sources provide a specified voltage regardless of the current flowing through the device. Ideal sources can, obviously, provide infinite power; all real sources will provide only limited power to the circuit. We will discuss non-ideal sources in later projects.
  • Ideal current sources provide a specified current regardless of the voltage difference across the device. Ideal current sources can, like ideal voltage sources, provide infinite power; all real sources will provide only limited power to the circuit; as with voltage sources, this is a topic for later projects.

Test Your Knowledge!

  1. A five volt ideal source is connected to a circuit element as shown. What do you think the voltage across the element, V, and the current through the element are? (This question is not entirely fair, since determining V requires use of Kirchhoff's voltage law, which isn't presented in this project. Take a guess, though, based on your gut feeling.)
  2. A two amp ideal source is connected to a circuit element as shown. What do you think the voltage across the element, V, and the current through the element are? (This question is not entirely fair, since determining I requires use of Kirchhoff's current law, which isn't presented in this project. Take a guess, though, based on your gut feeling.)
  3. What is the current, I, in the circuit below?
  4. What is the voltage V in the circuit below?
  5. A 3V ideal voltage source is connected across a perfect conductor. What do you think will happen? What if we reduce the voltage to 0.01 milli-volts?
  6. A 0.01 amp ideal current source is connected to an open circuit. What do you think will happen? (Note: an open circuit allows no current to flow.)

Selected Answers

  1. The voltage is 5V (the source requires that it provide 5V across its terminals. (The circuit element shares the same terminals as the voltage source, so it also has 5V across its terminals.) We don't know anything about the current, since we don't know anything about the electrical component to which the source is connected.
  2. The current is 2A (the source requires that it provide 2A. (There is nowhere for the current to go except the circuit element, so 2A also goes through the circuit element.) We don't know anything about the voltage, since we don't know anything about the electrical component to which the source is connected.
  3. Not enough is known about the circuit element to determine current. The ideal source can provide any current.
  4. Not enough is known about the circuit element to determine voltage.
  5. The voltage source requires that the voltage difference across the perfect conductor be 3V. The perfect conductor doesn't allow any voltage difference across it. The voltage source will deliver infinite current, in an attempt to create a voltage difference across the conductor. Reducing the voltage won't change this scenario.
  6. The current source requires that 0.01A flow through the open circuit, but the open circuit won't allow any current through it. The current source will create an infinite voltage across the open circuit, in an attempt to force current through the open circuit.


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