Parallel Resistance

Quick Reference​

Parallel Resistance Calculation​

TotalR = 1 / ∑(1 / Rn...Rn)

Resistors (or resistances) can be arranged in parallel, as in the following diagram:

Conductance; the Siemens (S)​

When resistors are arranged in this configuration, their total resistance is calculated by adding up the conductance, measured in siemens (S), which is defined as the reciprocal of resistance:

Siemens = 1 / Resistance in Ω

The letter G is often used to denote conductance/siemens, so the units calculate as follows:

G = 1/R
R = 1/G

Calculation​

Therefore, total resistance is calculated by:

TotalR = 1 / ∑(1 / Rn...Rn)

Calculation Steps​

To calculate the resistance of a parallel resistor network, we have to:

1. Convert each individual resistance to conductance
3. Convert the sum back to resistance

Example​

Let's consider the same resistor values we had in series, and calculate them in parallel:

• R1 - 100Ω
• R2 - 5Ω
• R3 - 1KΩ

First, we need to convert each value to siemens:

G1 = 1/100Ω = 0.01 S
G2 = 1/5Ω = 0.2 S
G3 = 1/1KΩ = 1/1000Ω = 0.001 S

Once we have their conductance, we add them to get the total conductance:

0.01 + 0.2 + 0.001 = 0.211 S

Converting from 0.211 siemens to ohms:

Resistance = 0.211 S = 1/0.211 = 4.74Ω

Total resistance with the same resistors as we had in series is now 4.7Ω in parallel.

Parallel Resistor Banks​

Sometimes, resistors in parallel come in banks of the same resistor values. In this case, there's a shortcut to calculate the total resistance:

Total Resistance = Resistance of Each Resistor / Number of Resistors

Therefore, (10), 5KΩ resistors in parallel would be:

5,000Ω / 10 = 500Ω

Common Voltage, Different Current​

In a parallel resistance circuit, the voltage at each resistor is the same, but the current flowing through each resistor is dependent on the amount of resistance that resistor has.

Power Calculation​

Since we know the voltage and resistance, we can use the P = V^2 / R form of the power calculation equation, and just as with series resistance, we add an n to specify power and resistance at resistor number n:

Pn = V^2 / Rn