Question

Here are three resistors in parallel. 4,12,6 If you need to, please assume they are hooked up to a 12 V power source. What is the total resistance of the circuit?

Three resistors in parallel

Answer 1

To find the total resistance (\( R_t \)) of three resistors connected in parallel, you can use the following formula:

\[
\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}
\]

In this case, the resistors \( R_1 \), \( R_2 \), and \( R_3 \) have values of 4 ohms, 12 ohms, and 6 ohms, respectively. Let's calculate the total resistance:

\[
\frac{1}{R_t} = \frac{1}{4} + \frac{1}{12} + \frac{1}{6}
\]

To do the addition of these fractions, we need a common denominator. The least common multiple (LCM) of 4, 12, and 6 is 12. Now, convert each fraction:

\[
\frac{1}{4} = \frac{3}{12}
\]
\[
\frac{1}{12} = \frac{1}{12}
\]
\[
\frac{1}{6} = \frac{2}{12}
\]

Now substitute these values into the equation:

\[
\frac{1}{R_t} = \frac{3}{12} + \frac{1}{12} + \frac{2}{12} = \frac{3 + 1 + 2}{12} = \frac{6}{12}
\]

Simplifying this gives:

\[
\frac{1}{R_t} = \frac{1}{2}
\]

Now take the reciprocal to find \( R_t \):

\[
R_t = 2 \, \text{ohms}
\]

Therefore, the total resistance of the circuit is **2 ohms**.