To produce the most thermal energy in the resistors, should they be connected in series or parallel?why?

Answer 1

Series, if you have a current source and parallel if you have a voltage source.

P = I^2 R
P = V^2/R

Answer 2

Parallel, for normal source of power.
Energy is I^2r
When the resistors are connected in parallel, there will be several parallel paths for the current. Each resistor will generate V^2/r thermal energy

If the resistors are connected in series, and the voltage source is the same, the curent will be very small, in such a way that the total voltage will get distributed in the ratio of each resistor.

Thermal energy contributed by each resistor will be v^2/r. Where v across each resistor is fraction of Source voltage V

It can be seen that each resistor will generate (V/v)^2 more thermal energy in parallel than in series.

Answer 3

There is no set answer to your question.

To produce the maximum output that a source is capable of, the impedance of the load should equal the impedance of the source. In an given situation, for any given set of resistors, this may require connections in series, parallel or some combination.

Only in the case of the idealized models of constant current and constant voltage sources can we make some kind of conclusion. For a constant-current source, you increase the power as the voltage increases. Therefore the resistors should be connected in series. For a constant-voltage source, you increase the power as the current increases. Therefore connect the resistors in parallel.

However, be aware that all physically-realizable "constant" current sources have a maximum voltage they can produce, and all physically-realizable "constant" voltage sources have a maximum current. So in reality, even for a "constant" current source, you can find a set of resistors for which you could get more power by connecting at least some of them in parallel.
Similarly for any "constant" voltage source that you can build or buy.

Answer 4

The answer, is parallel, assuming the voltage you apply is constant (which it usually is). The maximum thermal energy equates to the maximum power, so you need to calculate that with the power law:

P = V * I.

To calculate I, you need to know two things, how to find I when you know V and R (the resistor), and what happens to things in parallel and series.

The answer "series" or "no answer" is not correct and here is why.

You need to assume a constant voltage for both situations, and since this is common practice, a reasonable assumption.

Next, you need to know that items in parallel both receive the same voltage across them. A current flows though each item, as you add more items in parallel, you get more current (and more power too).

Lets look at this in terms of one resistor connected to a 10V source, and lets use a 1 ohm resistor. The numbers don't matter, but they will give something you can see easily.

One resistor 1 ohm, 10V, what is the current (this is ohms law)?

I = V / R = 10V / 1 ohm = 10 amps

What is the power? (multiply V times I):
10 amps * 10 V = 100W.

What if it were two resistors in parallel?

Both resistors get 10V, so its twice the current as each resistor consumes 10 amps. You can think of it a having two separate "pipes" if you want a water analogy. Two parallel pipes carry more water than one, twice as much if they are the same size.

The total resistance drops in 1/2 in this case so the math is:

10V / 0.5 ohms = 20 amps

or:

10V/ 1 ohm = 10 amps (PLUS) 10V / 1 ohm = 10 amps
= 20 amps (same answer)

Power is then 20 amps * 10V = 200 W (as mentioned earlier).


When you put resistors in series, you give the electricity a more difficult path. I like to think of this in human terms. Think of how much more work it is to run 2 miles compared to only 1. If you put two resistors end to end (in series), the current first has to flow though one, and then the next one, before getting back to the battery. So, in the case of two equal resistors, the current is cut in half, because the resistance doubled. Heres the math:

10V / (1 ohm + 1 ohm) = 10V/ 2 ohms = 5 amps.

And it gets worse, the voltage across the resistors is 10V BETWEEN the two of them, not 10V for each resistor. The voltage on each of the resistors in this case is exactly 1/2 the voltage, so your power on each resistor is:

P = V * I = 5V * 5A = 25W.

Its 1/4 the power due to 1/2 the voltage with 1/2 the current. Since you have two resistors though, each emits 25W, so you can add the power:

25W + 25W = 50W.

So...

Series is the coldest,
one single resistor is the next hottest
and resistors in parallel are the hottest.

Try it if you like, but I recommend using larger value resistors so the current and heat doesn't get out of hand. Try 1.5 to 10V with 100 ohm to 1k resistors, or for more fun, try light bulbs, it really shows the effect.

One last proof regarding series circuits. Just like if I asked you to run 100 miles you would be exhausted, taking this to its extreame is basically an open circuit, ie infinite resistance in engineering terms. Heres the math for that. Suppose 100, one ohm resistors...

10V / (100*1 ohm) = 10V / 100 = 0.1 A

The total voltage across ALL of those resistors is 10V, so the total power is 10V * 0.1A or 1W, about 100th that of a single resistor.

(If you did that in parallel, it would be 100 circuits of 10A each, or 1kA. 1kA * 10V would be 10kW or 10,000W.)

Lets take it one step further, a million resistors in series (or just one of a Megaohm - saves lots of wiring):

10V / 1M = 10 microamps

10 microamps * 10V = 100 microwatts (or 0.0001 W).

As you can see, more resistors in series, the more it looks like an open circuit. Makes sense doesn't it?

Any electrical text will tell you this, but here is a source:
http://physics.bu.edu/py106/notes/Circuits.html