A bulb is conneted to an ideal battery of emf 10 V so that the resulting current is 10 mA. When the bulb is connected to 220 V mains (ideal), the current is 50 mA. Choose the correct alternative (s)

Options

A. In the first case, the resistance of the bulb is `1KOmega` and in second case, it is `4.4KOmega`.
B. It is possible since ohm's law is not followed
C. The increase in resistance is due to heating of the filament of the bulb when it is conneted to 220 V mains
D. None of these

Answer

To solve the problem step by step, we will apply Ohm's Law and analyze the given information about the bulb's behavior under different voltage conditions.

### Step 1: Understand the Given Data
We have two scenarios for the bulb:
1. Connected to a 10 V battery, the current is 10 mA.
2. Connected to a 220 V mains supply, the current is 50 mA.

### Step 2: Calculate Resistance in the First Case
Using Ohm's Law, which states \( V = I \times R \), we can find the resistance in the first case.

- Given:
- Voltage \( V_1 = 10 \, \text{V} \)
- Current \( I_1 = 10 \, \text{mA} = 10 \times 10^{-3} \, \text{A} \)

Using the formula:
\[ R_1 = \frac{V_1}{I_1} = \frac{10 \, \text{V}}{10 \times 10^{-3} \, \text{A}} = \frac{10}{0.01} = 1000 \, \Omega = 1 \, \text{k}\Omega \]

### Step 3: Calculate Resistance in the Second Case
Now, we will calculate the resistance in the second case.

- Given:
- Voltage \( V_2 = 220 \, \text{V} \)
- Current \( I_2 = 50 \, \text{mA} = 50 \times 10^{-3} \, \text{A} \)

Using the formula:
\[ R_2 = \frac{V_2}{I_2} = \frac{220 \, \text{V}}{50 \times 10^{-3} \, \text{A}} = \frac{220}{0.05} = 4400 \, \Omega = 4.4 \, \text{k}\Omega \]

### Step 4: Analyze the Results
From our calculations:
- Resistance in the first case \( R_1 = 1 \, \text{k}\Omega \)
- Resistance in the second case \( R_2 = 4.4 \, \text{k}\Omega \)

### Step 5: Conclusion
Since the resistance changes from 1 kΩ to 4.4 kΩ when the voltage changes, we conclude that the resistance is not constant. This indicates that Ohm's Law is not being followed in this scenario.

### Step 6: Evaluate the Options
1. **First option**: Incorrect, as the resistance is not constant.
2. **Second option**: Correct, as Ohm's Law is not followed.
3. **Third option**: Correct, as the increase in resistance can be attributed to the heating of the filament when connected to a higher voltage.

### Final Answer
The correct alternatives are:
- Option 2: It is possible since Ohm's law is not followed.
- Option 3: The increase in resistance is due to heating of the filament of the bulb when it is connected to 220 V mains.

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