A 100 watt bulb working on 200 volt and a 200 watt bulb working on 100 volt have

Options

A. resistance in the ratio of `4:1`
B. maximum current ratings in the ratio of `1:4`
C. resistance in the ratio of `2:1`
D. maximum current ratings in the ratio of `1:2`

Answer

To solve the problem, we need to find the resistance and current ratings for both bulbs and then compare them. Let's break it down step by step.

### Step 1: Calculate the resistance of the 100-watt bulb (Bulb 1)
We know the power (P) and voltage (V) for Bulb 1:
- Power (P1) = 100 watts
- Voltage (V1) = 200 volts

Using the formula for resistance:
\[ R = \frac{V^2}{P} \]
Substituting the values:
\[ R_1 = \frac{200^2}{100} = \frac{40000}{100} = 400 \, \text{ohms} \]

### Step 2: Calculate the current for the 100-watt bulb (Bulb 1)
Using Ohm's law, we can find the current (I):
\[ I = \frac{V}{R} \]
Substituting the values:
\[ I_1 = \frac{200}{400} = \frac{1}{2} \, \text{amperes} \]

### Step 3: Calculate the resistance of the 200-watt bulb (Bulb 2)
Now, we know the power and voltage for Bulb 2:
- Power (P2) = 200 watts
- Voltage (V2) = 100 volts

Using the same formula for resistance:
\[ R_2 = \frac{V^2}{P} \]
Substituting the values:
\[ R_2 = \frac{100^2}{200} = \frac{10000}{200} = 50 \, \text{ohms} \]

### Step 4: Calculate the current for the 200-watt bulb (Bulb 2)
Using Ohm's law again to find the current:
\[ I_2 = \frac{V}{R} \]
Substituting the values:
\[ I_2 = \frac{100}{50} = 2 \, \text{amperes} \]

### Step 5: Determine the ratio of resistances
Now we can find the ratio of the resistances of the two bulbs:
\[ \text{Resistance ratio} = \frac{R_1}{R_2} = \frac{400}{50} = 8:1 \]

### Step 6: Determine the ratio of maximum current ratings
Now, we find the ratio of the maximum current ratings:
\[ \text{Current ratio} = \frac{I_1}{I_2} = \frac{\frac{1}{2}}{2} = \frac{1}{4} \]

### Conclusion
From the calculations:
- The resistance of the first bulb is 400 ohms and the second bulb is 50 ohms, giving a resistance ratio of 8:1.
- The current ratings are in the ratio of 1:4.

Thus, the correct answer is that the maximum current ratings are in the ratio of 1:4.