Question

If you have a parallel circuit with a battery (2 ohms), a light bulb (1 ohm), and a fan (3 ohms) what is your total resistance?

3 ohms

6 ohms

1.5 ohms

0.54 ohms

Answer 1

To find the total resistance in a parallel circuit, you can use the formula:

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

In your case:
- \(R_1 = 2 \, \text{ohms}\) (battery)
- \(R_2 = 1 \, \text{ohm}\) (light bulb)
- \(R_3 = 3 \, \text{ohms}\) (fan)

Substituting these values into the formula:

\[
\frac{1}{R_{total}} = \frac{1}{2} + \frac{1}{1} + \frac{1}{3}
\]

Calculating each term:

\[
\frac{1}{2} = 0.5
\]
\[
\frac{1}{1} = 1
\]
\[
\frac{1}{3} \approx 0.3333
\]

Now adding these together:

\[
\frac{1}{R_{total}} = 0.5 + 1 + 0.3333 \approx 1.8333
\]

Now take the reciprocal to find \(R_{total}\):

\[
R_{total} = \frac{1}{1.8333} \approx 0.545 \, \text{ohms}
\]

Rounding this gives approximately **0.54 ohms**.

Therefore, the correct answer is **0.54 ohms**.