Question

What is the equivalent resistance of two parallel resistors?

Answer 1

The equivalent resistance \( R_{\text{eq}} \) of two resistors in parallel is found using this formula:

\[
\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2}
\]

Where:

1. \( R_1 \) is the resistance of the first resistor
   

1. \( R_2 \) is the resistance of the second resistor
   

To find the equivalent resistance, you follow these steps:

1. Take the reciprocal (1 divided by the resistance value) of each resistor's resistance.
   

1. Add those values together.
   

1. Take the reciprocal of the result to find \( R_{\text{eq}} \).
   

Example:

Let’s say \( R_1 = 4 \, \Omega \) and \( R_2 = 6 \, \Omega \).

\[
\frac{1}{R_{\text{eq}}} = \frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}
\]

So,

\[
R_{\text{eq}} = \frac{12}{5} = 2.4 \, \Omega
\]

That’s the equivalent resistance for two parallel resistors. It will always be less than the smallest resistor in the parallel combination!