Formula for resistance in parallel circuit

In summary, the formula for resistance in a parallel circuit is the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of each individual resistor, which can also be written as a summation using the sigma notation.
  • #1
DB
501
0
My science teacher gave me this formula for resistance in parallel circuit.
[tex]\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...[/tex]

Thats exactly how he wrote it.
I would like this using the summation sigma

[tex]\frac{1}{R_{eq}}=\sum_{R=\frac{1}{R_n}}^n[/tex]

Is that right? I am sure it's not lol...
 
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  • #2
DB said:
My science teacher gave me this formula for resistance in parallel circuit.
[tex]\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...[/tex]

Thats exactly how he wrote it.
I would like this using the summation sigma

[tex]\frac{1}{R_{eq}}=\sum_{R=\frac{1}{R_n}}^n[/tex]

Is that right? I am sure it's not lol...

Not quite. You should write it as

[tex]\frac{1}{R_{eq}}=\sum_{i=1}}^n \frac{1}{R_i}[/tex]

Zz.
 
  • #3
[tex]\frac{1}{R_{eq}}=\sum_{i=1}^n \frac{1}{R_i}[/tex]

Where n is the number of resistors and i is just a dummy letter (a counter).
 

Related to Formula for resistance in parallel circuit

What is the formula for resistance in a parallel circuit?

The formula for resistance in a parallel circuit is Rtotal = 1 / (1/R1 + 1/R2 + 1/R3 + ... + 1/Rn), where Rtotal is the total resistance and R1, R2, R3, ... , Rn are the individual resistances in the circuit.

How do you calculate the total resistance in a parallel circuit?

The total resistance in a parallel circuit can be calculated using the formula Rtotal = 1 / (1/R1 + 1/R2 + 1/R3 + ... + 1/Rn). This involves taking the reciprocal of each individual resistance and adding them together, then taking the reciprocal of the sum to get the total resistance.

What is the effect of adding resistors in parallel?

Adding resistors in parallel decreases the total resistance in the circuit. This is because the current is divided between the different paths, resulting in a lower overall resistance. This is known as a "parallel resistance" or "conductance".

Can the total resistance in a parallel circuit ever be lower than the lowest individual resistance?

No, the total resistance in a parallel circuit can never be lower than the lowest individual resistance. This is because the total resistance is always the reciprocal of the sum of the reciprocals of the individual resistances, and the reciprocal of a number can never be smaller than the original number. In other words, the total resistance can only approach but never reach the lowest individual resistance.

What happens to the current in a parallel circuit when one resistor is removed?

When one resistor is removed from a parallel circuit, the total resistance decreases and the current increases. This is because there is one less path for the current to flow through, resulting in a lower overall resistance and a higher current. This relationship is described by Ohm's law, which states that current is directly proportional to voltage and inversely proportional to resistance.

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