To calculate the power P dissipated by a resistor R when a current I passes though it, we will use Joule's law of heating :. You can use any of the three formulas mentioned above to calculate the power dissipated by resistors. The power dissipated by a resistor appears in the form of heat, i. The maximum power that a resistor can dissipate without burning is called the power rating of a resistor. In a series circuit see figure 1 , the circuit's total resistance or equivalent resistance is the sum of the individual resistances.
If we connect a voltage source V , to this circuit, the same current I will flow sequentially through all the resistors.
We can calculate the total current in a series circuit using Ohm's law :. Let us consider a circuit consisting of parallel combination of resistors, R 1 , R 2 , We can determine the total resistance in a parallel circuit using the formula:.
If we connect a voltage source V across this combination, the total current in a parallel circuit is:. In parallel combination of resistors, the voltage drop across each resistor is the same. Hence we can calculate the power dissipation across each resistor as:. Let us see how to calculate power dissipation in a series circuit using the power dissipation calculator.
We will consider a circuit consisting of three resistors connected in series across a battery with a voltage output of You can also use this calculator just to calculate the total current in a parallel circuit or a series circuit.
A parallel circuit dissipates more power than a series circuit. For the same set of resistors, the total resistance of the parallel circuit is always lower than the total resistance in a series circuit. Since the power dissipated in a circuit is inversely proportional to the resistance of the circuit for a constant voltage source, a parallel connection will dissipate more power than a series circuit. In a series circuit , the highest value resistor dissipates the most power. This is because the same current sequentially flows through each resistor in a series connection, and the power dissipated is directly proportional to the resistance.
In regards to the laws of physics, if there is an increase in voltage E , then the current I will also increase, and the power dissipation of a resistor, will, in turn, increase as well.
In the field of electronics, power dissipation is also a measurement parameter that quantifies the releasing of heat within a circuit due to inefficiencies. As I mentioned earlier, each resistor has a power rating, and in terms of design, this allows designers to assess whether or not a particular resistor will meet their design needs within a circuit. Therefore, to calculate the power dissipated by the resistor, the formulas are as follows:. So, using the above circuit diagram as our reference, we can apply these formulas to determine the power dissipated by the resistor.
Generally speaking, no; however, there are some instances where heat dissipation is a good thing. Take, for example, electric heaters that use resistance wire such as Nichrome. Nichrome is a unique heating element due to its cost-effectiveness, resistance to the flow of electrons, strength, flexibility, resistance to oxidation, and stability in high temperatures. Also, another instance where heat dissipation is favorable is with incandescent light bulbs, which are in use as cost-effective heaters.
Overall, under normal circumstances, heat dissipation is not desirable, but on the rare occasions that it is, it will then consist of efforts to control the heat dissipation rather than moderate it. Ensure your resistor's power rating meets your circuit design needs. If you are designing PCBs, ensure your traces are large enough to keep resistance low and avoid excessive heating. When designing a switching circuit, be sure to keep your switching time short as much as possible.
To reduce switching times, make the slew rate as steep as possible, by reducing the capacitance on the line. When resistors are connected in parallel, more current flows from the source than would flow for any of them individually, and so the total resistance is lower.
The total resistance for a parallel combination of resistors is found using the equation below. Entering known values gives. Note that in these calculations, each intermediate answer is shown with an extra digit. We must invert this to find the total resistance R p. This yields. Current I for each device is much larger than for the same devices connected in series see the previous example.
A circuit with parallel connections has a smaller total resistance than the resistors connected in series. The power dissipated by each resistor can be found using any of the equations relating power to current, voltage, and resistance, since all three are known. The power dissipated by each resistor is considerably higher in parallel than when connected in series to the same voltage source. The total power can also be calculated in several ways. Note that both the currents and powers in parallel connections are greater than for the same devices in series.
More complex connections of resistors are sometimes just combinations of series and parallel. These are commonly encountered, especially when wire resistance is considered. In that case, wire resistance is in series with other resistances that are in parallel. Combinations of series and parallel can be reduced to a single equivalent resistance using the technique illustrated in Figure 4. Various parts are identified as either series or parallel, reduced to their equivalents, and further reduced until a single resistance is left.
The process is more time consuming than difficult. Figure 4. This combination of seven resistors has both series and parallel parts. Each is identified and reduced to an equivalent resistance, and these are further reduced until a single equivalent resistance is reached.
The simplest combination of series and parallel resistance, shown in Figure 4, is also the most instructive, since it is found in many applications. For example, R 1 could be the resistance of wires from a car battery to its electrical devices, which are in parallel. R 2 and R 3 could be the starter motor and a passenger compartment light. We have previously assumed that wire resistance is negligible, but, when it is not, it has important effects, as the next example indicates.
Figure 5 shows the resistors from the previous two examples wired in a different way—a combination of series and parallel. We can consider R 1 to be the resistance of wires leading to R 2 and R 3. Figure 5. These three resistors are connected to a voltage source so that R 2 and R 3 are in parallel with one another and that combination is in series with R 1.
To find the total resistance, we note that R 2 and R 3 are in parallel and their combination R p is in series with R 1. Thus the total equivalent resistance of this combination is. First, we find R p using the equation for resistors in parallel and entering known values:. The total resistance of this combination is intermediate between the pure series and pure parallel values Thus its IR drop is.
We must find I before we can calculate V 1. The voltage applied to R 2 and R 3 is less than the total voltage by an amount V 1. When wire resistance is large, it can significantly affect the operation of the devices represented by R 2 and R 3. To find the current through R 2 , we must first find the voltage applied to it. We call this voltage V p , because it is applied to a parallel combination of resistors. The voltage applied to both R 2 and R 3 is reduced by the amount V 1 , and so it is.
The current is less than the 2. The power is less than the One implication of this last example is that resistance in wires reduces the current and power delivered to a resistor. If wire resistance is relatively large, as in a worn or a very long extension cord, then this loss can be significant.
If a large current is drawn, the IR drop in the wires can also be significant. We conclude that both resistors in our example circuit consume power, which points to the voltage source as the producer of power. The current flowing into the source's positive terminal is -i out. Consequently, the power calculation for the source yields:. Confirm that the source produces exactly the total power consumed by both resistors.
This result is quite general: sources produce power and the circuit elements, especially resistors, consume it. But where do sources get their power? Again, circuit theory does not model how sources are constructed, but the theory decrees that all sources must be provided energy to work.
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