Resistors in Parallel

Adding resistors together to decrease their value

Resistors can be added together in parallel to create a smaller total resistance value.  Take R as the value for a resistor, where:

Rtotal = 1/(1/R1 + 1/R2 + 1/R3 + ... + 1/Rn)

As you can see, R_total is more complex to calculate in a parallel circuit than in a series circuit.  We have to first add together the inverse value of each resistor (1/R_x) and then take the inverse value of the resulting total to get R_total.  Unless you're really good at working out inverse values, it is a good idea to have a scientific calculator handy.

How does this formula work on real resistors?  If you needed a 510R resistor, you could connect two 1K resistors together as shown below.

The resulting value would be:

R_total = 1/(1/1000R + 1/1000R)

R_total = 1/(.001+.001)

R_total = 1/.002

R_total = 500R

The 500R value is within 5% of the desired 510R value, so this is acceptable.