Equivalent Resistance of Parallel Resistors

In summary, the formula for calculating equivalent resistance in parallel resistors is 1/Req = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn, where Req is the equivalent resistance and R1, R2, R3, etc. are the individual resistances. To determine the equivalent resistance when there are more than two parallel resistors, you can use this formula or the shortcut method of adding all the individual resistances together and taking the reciprocal. The purpose of calculating equivalent resistance is to simplify a circuit and make it easier to analyze. The equivalent resistance can never be lower than the smallest individual resistance, as adding more resistors in parallel will always decrease the overall resistance. This is
  • #1
archaic
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I did this for fun, if you want to do it in an unconventional way, this would be useful in programming.
For ##n## resistors in parallel:
$$R_{total}=\frac{\prod_{i=0}^{n-1} R_{i}}{\sum_{i=0}^{n-1}(\prod_{j=0}^{n-2} R_{i+j \mod n})}$$
 
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  • #2
archaic said:
, this would be useful in programming.
too complex compared to the more simple and conventional way
 
  • #3
... or use this. There is no need to re-invent the wheel.

https://www.allaboutcircuits.com/tools/parallel-resistance-calculator/

Zz.
 

1. What is the formula for calculating equivalent resistance in parallel resistors?

The formula for calculating equivalent resistance in parallel resistors is 1/Req = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn, where Req is the equivalent resistance and R1, R2, R3, etc. are the individual resistances.

2. How do I determine the equivalent resistance when there are more than two parallel resistors?

To determine the equivalent resistance when there are more than two parallel resistors, you can use the formula 1/Req = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn, where Req is the equivalent resistance and R1, R2, R3, etc. are the individual resistances. You can also use the shortcut method of simply adding all the individual resistances together and then taking the reciprocal.

3. What is the purpose of calculating equivalent resistance in parallel resistors?

The purpose of calculating equivalent resistance in parallel resistors is to simplify a circuit and make it easier to analyze. By combining multiple resistors into one equivalent resistor, we can use Ohm's law to calculate the current and voltage in the circuit more easily.

4. Can the equivalent resistance in parallel resistors ever be lower than the smallest individual resistance?

No, the equivalent resistance in parallel resistors can never be lower than the smallest individual resistance. This is because adding more resistors in parallel will always decrease the overall resistance. The equivalent resistance will approach but never reach the smallest individual resistance.

5. How does adding more resistors in parallel affect the overall resistance in a circuit?

Adding more resistors in parallel will always decrease the overall resistance in a circuit. This is because in parallel circuits, the current has multiple paths to flow through, thus reducing the overall resistance and making it easier for the current to flow.

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