# Parallel resistor equation.

1. Feb 16, 2009

### hl_world

I was trying to work out a way to calculate the combined resistance of more than 2 resistors in parallel. We all know the MAD rule for 2 resistors but does this equation work:

combined resistance = sum of resistance * # of resistors-2

I checked wikipedia and there was nothing there above 2 resistors.

2. Feb 16, 2009

### Redbelly98

Staff Emeritus
3. Feb 16, 2009

### ravioli

Ultimately the way you figure this out is $$\frac{1}{R_{equivalent}}=\frac{1}{R_1}+\frac{1}{R_2}...\frac{1}{R_n}$$. (After messing around with Latex, someone else posted this... I'll keep the rest of the post as is)

A way to derive the equation that's been posted is to realize that the voltage across each resistor is the same. Since we know the basic V=IR, we can figure out the current going to each resistor. The sum of the currents is going to be the same as the current of an equivalent resistance for the given voltage. So you get....

$$\frac{V}{R_1}+\frac{V}{R_2}+...+\frac{V}{R_n}=\frac{V}{R_{equivalent}}$$. From there, just divide out the voltage V.

4. Feb 16, 2009

### hl_world

The sum of the inverse resistance values. I didn't think of that. I went to the resistor page on Wikipedia. The equation I posted still works though, right?

5. Feb 16, 2009

### ravioli

Only if all of the resistors are the same. Even then, your equation reduces down to...

$$R_{equivalent}=\frac{R}{n}$$ where n is the number of resistors.

6. Feb 16, 2009

### hl_world

Wait a minute, something's wrong:
1-1+2-1+1-1 = 2.5

How can a path with 2 1Ω resistors give a higher value just by adding another path of resistance albeit double resistance?

7. Feb 16, 2009

### dancavallaro

It's the *inverse* of the sum of the inverses. So your equivalent resistance is not 2.5 Ω but 1/2.5 = 0.4 Ω.

8. Feb 16, 2009

### hl_world

Oh right; I see now. Thanks