Power and the Passive Convention

The Passive Convention: The power associated with any circuit element may be found as the product of the voltage drop across the element and the current within the element. That is, P = VI. Simple enough. This reading section addresses the question as to whether a given element dissipates or supplies power. The term "absorbs" is used synonomously with "disspates" and the term "provides" is used synonomously with "supplies".

The key to identifying whether a given element dissipates or supplies power is to determine whether the element abides by the passive convention within the circuit in question. Finally, verifying that power is conserved within a circuit -- power supplied equals power dissipated -- is a good way to check your power calculations.

Resistors are passive elements and by considering the polarity of the voltage drop across a resistor and the direction of the corresponding current within the resistor, we may appreciate the passive convention. Consider Figure 1 which shows a 1.5V battery connected to a 1000 Ohm resistor.

circuit with a resistor and voltage source

In such a simple circuit with but two elements, it should be clear that the battery provides energy to support charge flow and the resistor dissipates energy. While we are guaranteed that a resistor will never provide power, it could happen in a circuit with multiple sources that one or more of the sources will absorb power. How will we know in such cases? Understanding the passive convention is key. The circuit in Figure 2 is that of Figure 1 with the sketch of the 1.5 V battery replaced with a common circuit symbol; the direction of current has been labeled as has the voltage drop across the resistor.

The current, I, is directed clockwise in the circuit. It is important to understand that the value of the current is the same throughout this simple single-loop circuit. Notice too that the current is directed through the resistor from higher-to-lower potential. Recall that resistors never provide power and rather dissipate it. Therefore, if we find that the current in ANY element is directed through the element from high-to-low potential, the element in question dissipates (or perhaps stores) energy.

We now have the passive convention -- an element that obeys the passive convention has its current directed through the element from high-to-low potential.

Look now to the 1.5V battery, the current is directed from low-to-high potential through the battery. Clearly, this is opposite the passive convention and so the battery must provide power to the circuit. Using Ohm's law, we find that the current in the circuit is 1.5 mA (1.5V / 1000 Ohms). Recalling that the power associated with an element is simply the product of its voltage and current, we see that in the circuit of Figure 1 the resistor dissipates 2.25 mW and the battery supplies 2.25 mW. As expected, power is conserved. In the examples tab, we will consider two more complicated examples; you will be given a chance to practice in the "Your Turn" tab.

Let's consider the circuit shown in Figure 3. There are six generic circuit elements with the voltage difference across each element labeled as well as key currents. Calculating the value of the power associated with each element should be very straightforward -- we will simply multiply the appropriate voltage and current. Take a moment and reflect upon both the value of power associated with a given element as well as whether the element in the circuit of Figure 3 is providing or dissipating energy. When you feel confident in you reasoning, click the individual elements in Figure 3 to see if you are correct.

Element 1: (5V)(1A) = 5W of power. Notice how the current is directed from high-to-low potential through element 1. Since it obeys the passive convention in this circuit, element 1 absorbs 5W of power. Click the box to close.

Fig 3. - Six generic circuit elements wired in a circuit with voltage and currents shown. Click on a given element in the circuit of Figure 3 to see if you are correct in terms of the power associated with the element and whether it provides or absorbs power in the circuit.

Let's consider one more example. But before we do, it is important to understand that as we progress through the course we will come across circuits in which we will NOT immediately know the true polarities of voltage and directions of current. In such cases we will simply make an assumption as to voltage polarities and current directions and then meticulously follow one of the systematic methods we will study. It will happen on occasion that we may find a voltage and/or a current that is negative. What does this mean? It simply indicates that our original assumption on polarity of voltage or direction of current was incorrect -- no big deal. The circuit of Figure 4 has both a negative voltage and a negative current. Can you calculate the power values for all six elements? Can you figure out which elements dissipate power and which provide it? Think the problem through before checking the answers that may be found by clicking on the individual circuit elements of Figure 4. A final note on this example and what you may see elsewhere... While all powers will be quoted as positive values in this example, in some contexts you may find something like -5W providing. This would be the same as saying 5W absorbing.

Before you head to the "Your Turn" tab, verify that power is conserved in the circuit of Figure 4.