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resistors in parallel

Resistors in Parallel

In this article we talk about resistors in parallel, the equivalent resistance and the current divider rule for parallel connection of resistors. Let’s consider this circuit:

resistors in parallel

resistors in parallel and equivalent resistor (click to enlarge)

In circuit 1 we have two resistors R1 and R2 connected in parallel and in circuit 2 the equivalent resistance Rp. I is the total current, I1 is the current that flows through R1 and I2 is the current that flows through R2.

Using the Kirchhoff’s current law (KCL) in circuit 1

Ip = I1 + I2 or Ip = V/R1 + V/R2

for n resistors

Ip = I1 + I2 + … + In or Ip = V/R1 + V/R2 + … + V/Rn

Using the Ohm’s Law in circuit 1 and 2

Ip = V/Rp => Ip = V/R1 + V/R2

The equivalent resistance Rp for resistors in parallel

1/Rp = 1/R1 + 1/R2 + … + 1/Rn

So the current through R1 is

I1 = (Ip * Rp)/R1

The Current Divider Rule

Ix = (Ip * Rp)/Rx

where Ix is the current through the Rx.

For 2 resistors in parallel you can use this formula

Rp = (R1 * R2)/R1 + R2 (only for 2 resistors in parallel)

3 Comments

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  • kiranshashi

    Good article – But when should one consider Parallel Vs Serial.
    Some examples would help or some scenarios to explain this would be appreciated.

    • Jim Keith

      Good question. The answer is generally pragmatic in that you need a specific resistance and /or power rating, but have only a few miscellaneous resistor values available. Series connected is best for high voltage applications where the voltage exceeds the voltage (or power) rating of the individual resistor. Beyond that, either connection can increase the power dissipation. A series /parallel array provides additional possibilities for obtaining the desired resistance etc.

  • MR.OHM 1970

    Awesome Theory Here!!!

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