Three bulbs of `40 W , 60 W and 100 W` are connected in series with a `240 V` source.

Options

A. The potential difference will be maximum across the `40 W` bulb .
B. The current difference will be maximum in `100 W` bulb.
C. The resistance of the `40 W` bulb is minimum.
D. The current through the `60 W` bulb will be `0.1 A`.

Explanation

To solve the problem of three bulbs (40 W, 60 W, and 100 W) connected in series with a 240 V source, we will follow these steps:

### Step 1: Calculate the Resistance of Each Bulb
The resistance \( R \) of each bulb can be calculated using the formula:
\[ R = \frac{V^2}{P} \]
where \( V \) is the voltage (220 V, as per the standard supply) and \( P \) is the power rating of the bulb.

1. **For the 40 W Bulb**:
\[ R_{40} = \frac{220^2}{40} = \frac{48400}{40} = 1210 \, \Omega \]

2. **For the 60 W Bulb**:
\[ R_{60} = \frac{220^2}{60} = \frac{48400}{60} \approx 807 \, \Omega \]

3. **For the 100 W Bulb**:
\[ R_{100} = \frac{220^2}{100} = \frac{48400}{100} = 484 \, \Omega \]

### Step 2: Calculate the Total Resistance in the Circuit
The total resistance \( R_{total} \) in a series circuit is the sum of the individual resistances:
\[ R_{total} = R_{40} + R_{60} + R_{100} \]
Substituting the values:
\[ R_{total} = 1210 + 807 + 484 = 2501 \, \Omega \]

### Step 3: Calculate the Current in the Circuit
Using Ohm's law, the current \( I \) in the circuit can be calculated as:
\[ I = \frac{V_{total}}{R_{total}} = \frac{240}{2501} \approx 0.096 \, \text{A} \]

### Step 4: Calculate the Voltage Drop Across Each Bulb
Using the formula \( V = I \times R \), we can find the voltage drop across each bulb.

1. **For the 40 W Bulb**:
\[ V_{40} = I \times R_{40} = 0.096 \times 1210 \approx 116.16 \, V \]

2. **For the 60 W Bulb**:
\[ V_{60} = I \times R_{60} = 0.096 \times 807 \approx 77.51 \, V \]

3. **For the 100 W Bulb**:
\[ V_{100} = I \times R_{100} = 0.096 \times 484 \approx 46.38 \, V \]

### Step 5: Analyze the Results
- The voltage drop across the 40 W bulb is the highest, which confirms that it will have the maximum potential difference.
- The current through each bulb is the same, as they are in series.
- The resistance of the 40 W bulb is the highest among the three.

### Conclusion
From the analysis:
- The potential difference will be maximum across the 40 W bulb.
- The current through the 60 W bulb is approximately 0.096 A, which is less than 0.1 A.

### Final Answer
The correct option is that the potential difference will be maximum across the 40 W bulb.

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