*Question G5C03:
What is the total resistance of a 10-, a 20-, and a 50-ohm resistor connected in parallel?*  

*Correct Answer is  A: 5.9 ohms*  

### AI Response: (may contain errors)  

To find the total resistance of resistors connected in parallel, we use the formula:

$$
\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}
$$

where:
- $R_1 = 10 \, \text{ohms}$
- $R_2 = 20 \, \text{ohms}$
- $R_3 = 50 \, \text{ohms}$

Substitute the values into the formula:

$$
\frac{1}{R_{\text{total}}} = \frac{1}{10} + \frac{1}{20} + \frac{1}{50}
$$

Calculate each term:

- $\frac{1}{10} = 0.1$
- $\frac{1}{20} = 0.05$
- $\frac{1}{50} = 0.02$

Add these values together:

$$
\frac{1}{R_{\text{total}}} = 0.1 + 0.05 + 0.02 = 0.17
$$

Now, take the reciprocal to find $R_{\text{total}}$:

$$
R_{\text{total}} = \frac{1}{0.17} \approx 5.88 \, \text{ohms}
$$

Rounding to one decimal place, the total resistance is approximately 5.9 ohms.

### Why the Correct Answer is Correct:
- **5.9 ohms** is the closest approximation to the calculated total resistance of 5.88 ohms.

### Why the Other Choices are Incorrect:
- **0.17 ohms** (Choice B) is the reciprocal of the total resistance, not the resistance itself.
- **17 ohms** (Choice C) is incorrect because it does not match the calculated value for parallel resistors.
- **80 ohms** (Choice D) is incorrect as it suggests a series connection, not parallel.

This method shows how to calculate the total resistance for resistors in parallel, which is always less than the smallest individual resistance.