A three - way light bulb has three brightness settings ( low , medium , and high) but only two filaments . The two filaments are arranged in three settings, when connected across a `120 V` line and can dissipate `60 , 120 and 180 W`. Answer the following questions:
(i) Higher resistance filament only works for `60 W`
ii. Low resistance filament works for `120 W`
iii.Low resistance filament works for `60 W`
iv. High resistance filament works for `120 W`
v. Low and high resistance filaments in parallel for `180 W`
vi. Low and high resistance filament in series for `180 W`

Options

A. `I,ii, and v` are correct
B. `I, ii , and vi` are correct
C. `iii, iv, and v` are correct
D. `iii , iv , and vi` are correct

Explanation

To solve the problem regarding the three-way light bulb with two filaments, we will analyze each setting and determine the resistance of the filaments based on the power ratings provided.

### Step-by-Step Solution:

1. **Understanding Power and Resistance:**
The power \( P \) dissipated by a resistor can be expressed using the formula:
\[ P = \frac{V^2}{R} \]
where \( V \) is the voltage across the resistor and \( R \) is the resistance. Rearranging this formula gives us:
\[ R = \frac{V^2}{P} \]

2. **Calculating Resistance for Each Setting:**
Given that the voltage \( V = 120 \, V \):
- For the **60 W** setting (higher resistance filament):
\[ R_1 = \frac{120^2}{60} = \frac{14400}{60} = 240 \, \Omega \]
- For the **120 W** setting (low resistance filament):
\[ R_2 = \frac{120^2}{120} = \frac{14400}{120} = 120 \, \Omega \]

3. **Analyzing Each Statement:**
- **(i)** Higher resistance filament only works for **60 W**:
- This is **True** since \( R_1 \) corresponds to the 60 W setting.
- **(ii)** Low resistance filament works for **120 W**:
- This is **True** since \( R_2 \) corresponds to the 120 W setting.
- **(iii)** Low resistance filament works for **60 W**:
- This is **False** because the low resistance filament is designed for 120 W.
- **(iv)** High resistance filament works for **120 W**:
- This is **False** because the high resistance filament is designed for 60 W.
- **(v)** Low and high resistance filaments in parallel for **180 W**:
- This is **True**. When connected in parallel, the total power is the sum of the individual powers: \( 60 + 120 = 180 \, W \).
- **(vi)** Low and high resistance filaments in series for **180 W**:
- This is **False**. In series, the total resistance is higher, and thus the power would be less than 180 W.

4. **Final Answers:**
The correct statements are:
- (i) True
- (ii) True
- (iii) False
- (iv) False
- (v) True
- (vi) False

Thus, the correct options are **(i), (ii), and (v)**.