Ohm's law (i.e., I forgot my Algebra)

In summary, the conversation discusses the formula for resistance in a parallel circuit, which is given by R0=1/(1/R1) + (1/R2) = (R1 x R2)/(R1 + R2). It is explained that this formula is used because the current can flow in multiple paths in a parallel circuit, making it necessary to use the inverse of the sum of the individual resistances. The conversation also mentions that this formula can be simplified for just two resistors to Rt = (R1*R2) / (R1 + R2). It is clarified that this formula only applies to parallel circuits, and that for series circuits, the formula is simply Rt = R1 + R2. The conversation
  • #1
ASEmech
2
0
I'm an ASE certified Technician specializing in Brakes and Four-wheel Alignments. I'm going to go for my cert. in Electrical systems this fall. As I began my self-study in electrical systems, I realized...I forgot my Algebra.

I'm currently studying Ohm's Law. Within Ohm's Law, I'm studying Resistance in a parallel circuit. The formula I'm given is:

R0=1/(1/R1) + (1/R2) = (R1 x R2)/(R1 + R2)

...where R0 (read R-sub0) is a combination of resistances R-sub1 and R-sub2.

I thought the sum of the resistances in any circuit was R0=R1+R2. Why is 1 divided by (1/R1) + (1/R2) and in the "denominator portion" of the formula, why is 1 divided by R1 (same question for 1 divided by R2) and then added to 1/R2? Also, how do you get from R0=1/(1/R1) + (1/R2) to (R1 x R2)/(R1 + R2)?
 
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  • #2
For resistors in series Rt = R1 + R2
In parallel it's 1/Rt = 1/R1 + 1/R2

For just a pair of resistors you can simplify this to
Rt = (R1*R2) / (R1 + R2)
 
  • #3
This thread probably belongs in the EE forum.
Anyway,

[itex]R_{tot}=R_1+R_2 [/itex] is only correct if the resistors are connected in series. In
a parallell ciruit the current can flow in several branches at once which is why you need to use the [itex]1/R_{tot}=1/R_1+...[/itex] formula.
This makes sense if you think about. Let's say you have two 1K resistors connected in parallell; now the current can flow via two different paths and since the resistors have the same value each one will carry half the current; plugging two 1K resistors into the formula for parallel resistors you will see that you end up with an equivalent resistance of 500 ohm. This is what you would expect since the two paths make "half as difficult" for the current to flow; i.e. connecting resistors in parallel REDUCES the total resistance.

You can derive the formula yourself by just using ohms law and remembering that the voltage across each of the resistors must be the same since they are connected in series.

Also

1/R=1/R1+1/R2 =R2/(R1*R2)+R1/(R2*R1=(R1+R2)/(R1*R2)
i.e.
1/R=(R1+R2)/(R1*R2)
meaning R=R1*R2/(R1+R2),
 
  • #4
Thanks, guys. I put this here because when I first saw this formula the first thing I thought of was Alg. 1.

Thanks again!
 

Related to Ohm's law (i.e., I forgot my Algebra)

1. What is Ohm's law?

Ohm's law is a fundamental law in physics that describes the relationship between voltage, current, and resistance in an electrical circuit. It states that the current flowing through a conductor is directly proportional to the voltage and inversely proportional to the resistance.

2. How is Ohm's law represented mathematically?

The mathematical representation of Ohm's law is V = IR, where V is voltage in volts, I is current in amperes, and R is resistance in ohms.

3. How do I use Ohm's law to solve for voltage?

To solve for voltage, use the formula V = IR and plug in the values for current and resistance. For example, if the current is 2 amps and the resistance is 10 ohms, the voltage would be 2 x 10 = 20 volts.

4. Can Ohm's law be applied to all electrical circuits?

Ohm's law is applicable to most electrical circuits, as long as the temperature and other environmental factors remain constant. However, there are some circuits where the relationship between voltage, current, and resistance may not follow Ohm's law.

5. What are some real-life applications of Ohm's law?

Ohm's law has various applications in everyday life, such as in household appliances, lighting systems, and electronic devices. It is also used in industries for designing and troubleshooting electrical circuits and in power distribution systems.

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