Hi Ron, sorry for the delay, I'll post the text first and then try to attach the diagrams (I'll correct any errors as they arise).
Very good, let's talk about a specific case and make practical assumptions.
With a voltage of 7.2 volts, you can choose from several solutions:
1. PARALLEL CONNECTION (ONE RESISTOR FOR EACH LED)
With one resistor for each LED (and then all the LED-resistor branches connected in parallel to the battery), the calculation is easy (see diagram no. 1).
To find the correct resistance value, simply apply the inverse formula of Ohm's law, and then:
R=V/I
The unknowns are the current intensity and the voltage.
Regarding the current, the value is given by the LED's factory data.
If I remember correctly (but I recommend always checking the datasheet for each component you use, it's important), the values โโfor 3 mm electronic bulb LEDs range from 15 mA to 20 mA (i.e., 0.015 A and 0.018 A). With 15 mA, you'll get a dimmer light but less heat loss and a longer LED lifespan; vice versa, with 20 mA.
The value I'll consider for the following calculations is 18 mA (0.018 A).
Regarding voltage, the value to consider won't be the battery voltage, because the LED voltage drop must be taken into account. So, battery voltage minus LED voltage drop.
Again, the LED voltage drop is a factory setting.
For these types of LEDs, the typical voltage drops are: 2 volts for red, 2.2 volts for yellow and green, and 3 volts for blue. Check the datasheet to be sure before proceeding.
With all the data available, you can apply Ohm's law:
R = (Vbatt - Vled) / I
With a red LED, we have:
R = (7.2 - 2) / 0.018 = 5.2 / 0.018 = 289 Ohms
At this point, you'll need to find the most suitable commercial resistor for this resistance value.
1.1 CHOOSING THE MOST SUITABLE COMMERCIAL RESISTOR FOR THE THEORETICAL VALUE
With the most common commercial series, you have two available values: 270 Ohm and 300 Ohm.
If you choose the 270 Ohm commercial resistor, you will have higher current (19 mA or 0.019 A) almost at the limit, and greater brightness.
If you choose the 300 Ohm commercial resistor, you will have lower current (17 mA or 0.017 A) almost at the limit, and greater brightness.
There are precision series that are much closer to the theoretical value, but I don't think there's any need; you can easily choose between them.
2. PARALLEL CONNECTION (EACH BRANCH HAS TWO LEDS IN SERIES WITH A RESISTOR)
(See diagram number 2).
In this case, the same calculations apply, but since there are two LEDs in series, the voltage drop to be considered will be the sum of the two, so 2 + 2 = 4 Volts.
R = (Vbatt - Vled1 - Vled2) / I
With a red LED, we have:
R = (7.2 - 4) / 0.018 = 3.2 / 0.018 = 178 Ohms
At this point, you'll need to find the most suitable commercial resistor for this resistance value, which, luckily, is 178 Ohms.
3. PARALLEL CONNECTION (EACH BRANCH HAS THREE LEDS IN SERIES WITH A RESISTOR)
(SEE diagram number 3).
In this case, the same calculations apply, but since there are three LEDs in series, the voltage drop to be considered will be the sum of the three, so 2 + 2 + 2 = 6 Volts.
R = (Vbatt-Vled1 โVled2 โ Vled3)/I
With a red LED, we have:
R = (7.2 -6) / 0.018 = 1.2/0.018 = 67 Ohms
At this point, you'll need to find the most suitable commercial resistor for this resistance value, which is 68 Ohms.
For obvious reasons, we can't connect four LEDs in series because the sum of their voltage drops is greater (8 Volts) than the supply voltage (7.2).
4. SUMMARY OF RESISTORS TO BE USED
With a single LED per resistor, use a 270 Ohm resistor.
With two LEDs per resistor, use a 178 Ohm resistor.
With three LEDs per resistor, use a 68 Ohm resistor.
There is a slight difference between red and green LEDs.
5. CONSIDERATIONS ON TOTAL CURRENT DRAWN BY THE CIRCUIT
For simplicity's sake, let's assume you want to power twelve LEDs with a 7.2 Volt battery (I'm using twelve LEDs for example only).
If you connect them all in parallel, you'll have a total current draw of 216 mA or 0.216 A (i.e., 0.18 mA x 12).
(See diagram 4.)
If you connect them in groups of two in parallel, you'll have a total current draw of 108 mA or 0.108 A (i.e., 0.18 mA x 6, because there are six branches in parallel).
(See diagram 5.)
If you connect them in groups of four in parallel, you'll have a total current draw of 72 mA or 0.072 A (i.e., 0.18 mA x 4, because there are four branches in parallel).
(See diagram 6.)
When you connect an LED in series with another, one of the two that breaks will prevent the current from flowing to the other, which will therefore appear off even if it's healthy.