A 25 W, 220V bulb and 100W, 220V bulb are joined in series and connected to the mains. Which bulb will glow brighter-

Options

A. 25 W bulb
B. 100 W bulb
C. first 25 W bulb and then 100 W bulb
D. Both will glow with same brighteness

Answer

To determine which bulb will glow brighter when a 25 W, 220 V bulb and a 100 W, 220 V bulb are connected in series, we can follow these steps:

### Step 1: Calculate the Resistance of Each Bulb
The power \( P \) of a bulb can be expressed in terms of voltage \( V \) and resistance \( R \) using the formula:
\[ P = \frac{V^2}{R} \]
From this, we can rearrange to find the resistance:
\[ R = \frac{V^2}{P} \]

### Step 2: Calculate the Resistance of the 25 W Bulb
For the 25 W bulb:
- Power \( P_1 = 25 \, \text{W} \)
- Voltage \( V = 220 \, \text{V} \)

Using the formula:
\[ R_1 = \frac{220^2}{25} = \frac{48400}{25} = 1936 \, \Omega \]

### Step 3: Calculate the Resistance of the 100 W Bulb
For the 100 W bulb:
- Power \( P_2 = 100 \, \text{W} \)
- Voltage \( V = 220 \, \text{V} \)

Using the same formula:
\[ R_2 = \frac{220^2}{100} = \frac{48400}{100} = 484 \, \Omega \]

### Step 4: Compare the Resistances
Now we have:
- \( R_1 = 1936 \, \Omega \) (for the 25 W bulb)
- \( R_2 = 484 \, \Omega \) (for the 100 W bulb)

Since \( R_1 > R_2 \), the 25 W bulb has a higher resistance than the 100 W bulb.

### Step 5: Determine the Current in the Series Circuit
In a series circuit, the same current \( I \) flows through both bulbs. The power consumed by each bulb can be calculated using:
\[ P = I^2 R \]

### Step 6: Calculate the Power Dissipated by Each Bulb
The power dissipated by each bulb can be expressed as:
- For the 25 W bulb:
\[ P_1 = I^2 R_1 \]
- For the 100 W bulb:
\[ P_2 = I^2 R_2 \]

### Step 7: Compare the Power Dissipated
Since \( R_1 > R_2 \), it follows that:
\[ P_1 > P_2 \]
This means the 25 W bulb will dissipate more power than the 100 W bulb when connected in series.

### Conclusion
Thus, the 25 W bulb will glow brighter than the 100 W bulb when connected in series.

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