# Parallel resistor equation.

• hl_world
In summary, the equation that's been posted does work for calculating the combined resistance of more than 2 resistors in parallel. However, if all of the resistors are the same, the equation reduces down to the simpler equation of R=n.

#### 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.

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.

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?

hl_world said:
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?

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.

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?

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.

Oh right; I see now. Thanks

## 1. What is the formula for calculating total resistance in a parallel circuit?

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

## 2. How do you calculate the equivalent resistance of two resistors in parallel?

To calculate the equivalent resistance of two resistors R1 and R2 in parallel, use the formula Req = (R1 x R2)/(R1 + R2).

## 3. What is the benefit of using parallel resistors in a circuit?

The benefit of using parallel resistors in a circuit is that it allows for multiple paths for current to flow, resulting in a decrease in the total resistance and an increase in the overall current of the circuit.

## 4. Can the total resistance in a parallel circuit ever be lower than the smallest individual resistance?

No, the total resistance in a parallel circuit can never be lower than the smallest individual resistance. However, it can approach the smallest resistance as more resistors are added in parallel.

## 5. How do you calculate the total current in a parallel circuit?

To calculate the total current in a parallel circuit, use the formula It = I1 + I2 + I3 + ... + In, where It is the total current and I1, I2, I3, ... In are the individual currents in each branch of the parallel circuit.