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 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, I[SUB]1[/SUB] is the current that flows through R1 and I[SUB]2[/SUB] is the current that flows through R2.
Using the Kirchhoff’s current law (KCL) in circuit 1
For 2 resistors in parallel you can use this formula
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, I[SUB]1[/SUB] is the current that flows through R1 and I[SUB]2[/SUB] is the current that flows through R2.
Using the Kirchhoff’s current law (KCL) in circuit 1
I[SUB]p[/SUB] = I[SUB]1[/SUB] + I[SUB]2[/SUB] or I[SUB]p[/SUB] = V/R1 + V/R2
for n resistors
I[SUB]p[/SUB] = I[SUB]1[/SUB] + I[SUB]2[/SUB] + … + I[SUB]n[/SUB] or I[SUB]p[/SUB] = V/R1 + V/R2 + … + V/Rn
Using the Ohm’s Law in circuit 1 and 2
I[SUB]p[/SUB] = V/Rp => I[SUB]p[/SUB] = 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
I[SUB]1[/SUB] = (I[SUB]p[/SUB] * Rp)/R1
The Current Divider Rule
I[SUB]x[/SUB] = (I[SUB]p[/SUB] * 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)