Two bulbs of (40 W, 200 V) and (100 W, 200 V). Then correct relation for their resistance:

Options

A. `R_(40) lt R_(100)`
B. `R_(4) gt R_(100)`
C. `R_(40) = R_(100)`
D. Non relation can be predicted

Explanation

To find the correct relation for the resistances of two bulbs rated at (40 W, 200 V) and (100 W, 200 V), we can follow these steps:

### Step 1: Understand the given data
We have two bulbs:
- Bulb 1: Power (P₁) = 40 W, Voltage (V) = 200 V
- Bulb 2: Power (P₂) = 100 W, Voltage (V) = 200 V

### Step 2: Use the power formula to find resistance
The power of an electrical device is given by the formula:
\[ P = \frac{V^2}{R} \]
Where:
- \( P \) is the power in watts,
- \( V \) is the voltage in volts,
- \( R \) is the resistance in ohms.

We can rearrange this formula to find resistance:
\[ R = \frac{V^2}{P} \]

### Step 3: Calculate the resistance of the first bulb (R₁)
Using the values for the first bulb:
\[ R₁ = \frac{V^2}{P₁} = \frac{200^2}{40} \]

Calculating this:
\[ R₁ = \frac{40000}{40} = 1000 \, \Omega \]

### Step 4: Calculate the resistance of the second bulb (R₂)
Using the values for the second bulb:
\[ R₂ = \frac{V^2}{P₂} = \frac{200^2}{100} \]

Calculating this:
\[ R₂ = \frac{40000}{100} = 400 \, \Omega \]

### Step 5: Compare the resistances
Now we have:
- \( R₁ = 1000 \, \Omega \)
- \( R₂ = 400 \, \Omega \)

To find the relation between the two resistances:
\[ R₁ > R₂ \]
Thus, we can conclude:
\[ R_{40W} > R_{100W} \]

### Final Answer
The correct relation for their resistance is:
\[ R_{40W} > R_{100W} \]

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