Three bulbs of 40, 60 and 100 watt are connected in series with the source of 200 volt. Then which of the bulb will be glowing the most –

Options

A. 100 watt
B. 60 watt
C. 40 watt
D. All are glowing equally

Answer

To determine which bulb will glow the most when three bulbs of 40W, 60W, and 100W are connected in series to a 200V source, we need to analyze the resistance of each bulb and how it relates to their power ratings.

### Step-by-Step Solution:

1. **Understand the relationship between power, voltage, and resistance**:
The power \( P \) of a bulb can be expressed in terms of voltage \( V \) and resistance \( R \) using the formula:
\[ P = \frac{V^2}{R} \]
Rearranging this gives us:
\[ R = \frac{V^2}{P} \]

2. **Calculate the resistance of each bulb**:
Since all bulbs are connected in series, we will calculate the resistance for each bulb using the voltage of 200V.

- For the 40W bulb:
\[ R_{40} = \frac{200^2}{40} = \frac{40000}{40} = 1000 \, \Omega \, (1 \, k\Omega) \]

- For the 60W bulb:
\[ R_{60} = \frac{200^2}{60} = \frac{40000}{60} \approx 666.67 \, \Omega \, (0.67 \, k\Omega) \]

- For the 100W bulb:
\[ R_{100} = \frac{200^2}{100} = \frac{40000}{100} = 400 \, \Omega \]

3. **Compare the resistances**:
Now we have the resistances:
- \( R_{40} = 1000 \, \Omega \)
- \( R_{60} \approx 666.67 \, \Omega \)
- \( R_{100} = 400 \, \Omega \)

From these calculations, we see that:
\[ R_{40} > R_{60} > R_{100} \]

4. **Determine which bulb will glow the most**:
In a series circuit, the current is the same through all components. The heat generated (and thus the brightness of the bulb) is directly proportional to the resistance of the bulb. Therefore, the bulb with the highest resistance will glow the most.

Since \( R_{40} \) is the highest, the 40W bulb will glow the most.

### Conclusion:
The bulb that will be glowing the most is the **40W bulb**.

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