*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:

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

where:
- $R_1 = 10 \, \Omega$
- $R_2 = 20 \, \Omega$
- $R_3 = 50 \, \Omega$

Now, substituting the values into the formula:

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

Calculating each term:

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

Now, adding these values together:

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

To find $R_{total}$, take the reciprocal:

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

Rounding gives us approximately $5.9 \, \Omega$, which is the correct answer.

### Explanation of Choices:
- **A: 5.9 ohms** (Correct)
  - This is the calculated total resistance for the given resistors in parallel.

- **B: 0.17 ohms** 
  - This value represents the sum of the reciprocals, not the total resistance itself. It is a common mistake to confuse the sum of reciprocals with the total resistance.

- **C: 17 ohms** 
  - This value does not correspond to any calculation related to the resistors in parallel. It may be mistakenly thought of as an average or some other calculation.

- **D: 80 ohms** 
  - This value is incorrect as it suggests a series connection of the resistors, which is not the case here. In series, the total resistance would be the sum of the individual resistances.

### Summary:
- Use the parallel resistance formula to find the total resistance.
- Remember to take the reciprocal of the sum of the reciprocals to find the total resistance in parallel circuits.