*Question G5C04:
What is the approximate total resistance of a 100- and a 200-ohm resistor in parallel?*  

*Correct Answer is  D: 67 ohms*  

### AI Response: (may contain errors)  

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

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

where:
- $R_1 = 100 \, \text{ohms}$
- $R_2 = 200 \, \text{ohms}$

Substitute the values into the formula:

$$
\frac{1}{R_{\text{total}}} = \frac{1}{100} + \frac{1}{200}
$$

Calculate each term:

- $\frac{1}{100} = 0.01$
- $\frac{1}{200} = 0.005$

Add these values:

$$
\frac{1}{R_{\text{total}}} = 0.01 + 0.005 = 0.015
$$

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

$$
R_{\text{total}} = \frac{1}{0.015} \approx 66.67 \, \text{ohms}
$$

This rounds to approximately 67 ohms, which is the correct answer (Choice D).

**Why the other choices are incorrect:**

- **Choice A: 300 ohms**  
  This would be the result if the resistors were in series, not parallel. In series, you simply add the resistances: $100 + 200 = 300$ ohms.

- **Choice B: 150 ohms**  
  This is the average of the two resistances, not the parallel resistance. It does not apply to parallel circuits.

- **Choice C: 75 ohms**  
  This is incorrect because it does not match the calculated parallel resistance. It might be a guess based on the values given.

Remember, for resistors in parallel, the total resistance is always less than the smallest individual resistance.