Calculating Resistance Equivalence

Once the design resistor value is calculated, all that’s left is to build the circuit. However, the resistor value may not match common resistor values available. In that case, a combination of resistors can be used to produce an equivalent value.

Series Resistors

Resistors in series can be summed:

R = R_1 + R_2

Parallel Resistors

Resistors in parallel are summed by their inverses:

1/R = 1/R_1 + 1/R_2

Example

It happens that we need a 150\Omega resistor for the yellow LED circuit, but suppose we have a bunch of 100\Omega resistors. How can they be combined to make a 150\Omega equivalent?

If we put two of them in series, they add… so that is 200\Omega, which is too much. On the other hand, two in parallel becomes 50\Omega. By making a circuit with one of these resistors in series with a pair in parallel, we will have a total of 100\Omega + 50\Omega=150\Omega, which is just right.

Quiz 2: Equivalent Resistance