Multiple resistors in series instead of using a single resistor has any advantage: heat produced by the resistors of diffent watts are different?

Question

I have two doubts, requesting you to answer my doubts separately. :)

1) I need a resistance of 'X', so is it better to use a single resistor of 'X' value or multiple resistance of r1+r2+r3='X'? What I mean is using multiple resistors in series instead of using a single resistor has any advantage? Will it reduce the resistors getting overheated?

2) Consider a 1W 2k2 resistor and a 1/4W 2k2 resistor. Is the heat produced by resistors of different watts different? Which resistor will get more heated in the same conditions (I mean the current, voltage etc given both resistors are same)

Regards, Kiran.

Answer 1

The 1 W resistor will get less hot that the 1/4 W resistor if they both dissipate the same power. The specific heat may be comparable, but because of the higher mass the 1 W resistor will need more power to get the same temperature rise.

You may need to place several resistors in series to prevent overheating. suppose you have a 1 kΩ/ 1/4 W resistor which has 20 V across it. Then the power will be (20 V)\$^2\$/ 1 kΩ = 400 mW, which is more than the 1/4 W the resistor is rated for, and which will reduce the resistor's life. You can use a 1 W version instead or for instance three 330 Ω/ 1/4 W resistors in series. Each will then dissipate only 130 mW, so that's a safe value.

Note that resistors can only dissipate their rated power at low temperatures. Most must be derated above 70 °C environment temperature, which means that the higher you go beyond that temperature the less power it may dissipate, until its maximum temperature, where the allowed dissipation becomes zero.

Apart from spreading power you also may need a couple of series resistors for high voltage applications. A resistor may be rated at 160 V, then you can't use it for 230 V, even if the current (and thus power) are very low. 230 V AC is 325 V peak, so you'll need 3 resistors in series.

Answer 2

It is possible to build a resistor with resistance R, capable of dissipating W watts, by combining n resistors of value R/n in series or R*n in parallel; in either case, the resistors must individually be capable of dissipating W/n watts even when in close proximity. One could also combine different values of resistors in series or parallel, but the share of power dissipated by each resistor would be proportional to its resistance for series-wired resistors, or inversely-proportional to its resistance for parallel wired.

In many cases, it won't matter whether resistors are wired in series or parallel; one could make the decision based upon the availability of the desired resistor values. There are a few cases where it may make a difference, however:

• If resistors are wired in series, the voltage across each resistor will be a fraction of the voltage across the whole string. By contrast, with parallel-wired resistors, every resistor will see the whole voltage. If one needs a resistor which can handle 1,000 volts, one could build it out of ten 200-volt resistors wired in series (note that it's good to leave some safety margin when doing such things). Wiring resistors in parallel offers no such benefit.

• If resistors are wired in series, a resistor which fails open will cause the whole string to fail open; a resistor which fails shorted will reduce the resistance of the string by its share of the resistance. If resistors are wired in parallel, a resistor which fails open will increase the resistance of the whole string, but a resistor which fails shorted will cause the whole string to fail shorted. In some cases, one or the other type of failure may have unacceptable safety implications. Note that if a resistor string pushed to its voltage limit, and if resistors fail shorted under overvoltage conditions (which is common), then when one resistor fails it may increase the voltage seen by other resistors, causing all of them to fail (thus the need for a safety margin).

• If resistors are wired in parallel, and their resistance increases with heat (as is typical), and one resistor starts getting hotter than the others, the share of power dissipated by that resistor will be reduced, thus causing other resistors to take up more of the load. By contrast, if such resistors are wired in series, a resistor which gets hotter than the others will increase its share of the power dissipation. This effect is generally not severe enough to cause thermal runaway, but generally means that one should provide some safety margin on resistor ratings (e.g. if one needs to dissipate 8 watts with series-wired resistors, it may be good to use ten one-watt resistors in series; one resistor may end up dissipating more than its 0.8-watt share of power, but even if one resistor ends up dissipating 25% more than it should, it would still be below one watt.

Often, it won't really matter whether one puts resistors in series or parallel. If the number of resistors one wants to use happens to be a perfect square, one may build a resistor of value R using n^2 resistors of that same value. Either wire n series strings of n resistors in parallel, or wire n bunches of n parallel resistors in series. Both approaches will offer the same resistance, voltage, and power ratings; the differences will be in their failure modes and load-sharing behavior.

Answer 3

On #2, my understanding is that both resistors will produce the same amount of heat. A 1W resistor is designed to both dissipate and tolerate the higher heat levels better than a 1/4W resistor, at the tradeoff of higher cost and a larger package.

I hope this is the case anyway, because I'm about to build a device using 12x 1ohm 10W resistors that's designed solely to get hot.

Answer 4

Think in terms of voltage drop. If you have a 10 volt supply with a 1 ohm resistor in series with a 9 ohm resistor connected to it, there will be 1 volt dropped across the 1 ohm resistor and 9 volts dropped across the 9 ohm resistor. The total resistance (ignoring the minute resistance of cables and jointing) will be 10 ohms. Ohms law tells us that the current in the circuit is 1 Amp. Power, which is what makes the heat, is the product of current and voltage so there will be 9 watts dissipated in the 9 Ohm resistor but only 1 in the 1 Ohm resistor. This is a little counter intuitive at first but think of the larger resistance as having a larger voltage supply than the smaller. Current is always the same anywhere in a series circuit so the larger one must dissipate more heat. If you were to hook these resistors to the same supply individually, the smaller resistance would dissipate more heat as more current would be able to pass through it.