Two bulbs of 500 W and 250 W are manufactured to operate on a 230 V line. If their resistances are `R_1` and `R_2` respectively, then `R_1//R_2` is:

Options

A. `1/2`
B. `2`
C. `1/3`
D. `1/5`

Explanation

To solve the problem, we need to find the equivalent resistance of two bulbs with given power ratings when connected in parallel. The power ratings of the bulbs are 500 W and 250 W, and they operate on a 230 V line.

### Step-by-Step Solution:

1. **Identify the given values:**
- Power of the first bulb (P1) = 500 W
- Power of the second bulb (P2) = 250 W
- Voltage (V) = 230 V

2. **Use the formula for resistance in terms of power:**
The resistance (R) of a device can be calculated using the formula:
\[ R = \frac{V^2}{P} \]
where \( V \) is the voltage and \( P \) is the power.

3. **Calculate the resistance of the first bulb (R1):**
\[ R_1 = \frac{V^2}{P_1} = \frac{(230)^2}{500} \]

4. **Calculate the resistance of the second bulb (R2):**
\[ R_2 = \frac{V^2}{P_2} = \frac{(230)^2}{250} \]

5. **Find the ratio of the resistances (R1/R2):**
\[ \frac{R_1}{R_2} = \frac{\frac{(230)^2}{500}}{\frac{(230)^2}{250}} = \frac{250}{500} = \frac{1}{2} \]

6. **Conclusion:**
The ratio of the resistances \( R_1 // R_2 \) is \( \frac{1}{2} \).

### Final Answer:
\[ R_1 // R_2 = \frac{1}{2} \]