A `25 W, 220 V` bulb and a `100 W , 220 V` bulb are connected in series across a `220 V` line , which electric bulb will glow brightly?

Options

A. `25 W` bulb
B. `100 W` bulb
C. Both will have equal incandescence.
D. Neither will give light.

Explanation

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 across a 220 V line, we can follow these steps:

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

#### For the 25 W bulb:
- \( P = 25 \, \text{W} \)
- \( V = 220 \, \text{V} \)

Calculating the resistance:
\[ R_{25} = \frac{(220)^2}{25} = \frac{48400}{25} = 1936 \, \Omega \]

#### For the 100 W bulb:
- \( P = 100 \, \text{W} \)
- \( V = 220 \, \text{V} \)

Calculating the resistance:
\[ R_{100} = \frac{(220)^2}{100} = \frac{48400}{100} = 484 \, \Omega \]

### Step 2: Analyze the Series Circuit
In a series circuit, the same current (I) flows through both bulbs. The total resistance (R_total) in the circuit is the sum of the individual resistances:
\[ R_{total} = R_{25} + R_{100} = 1936 \, \Omega + 484 \, \Omega = 2420 \, \Omega \]

### Step 3: Calculate the Current in the Circuit
Using Ohm's law, we can find the current flowing through the circuit:
\[ I = \frac{V_{total}}{R_{total}} = \frac{220 \, \text{V}}{2420 \, \Omega} \approx 0.0909 \, \text{A} \]

### Step 4: Calculate the Power Dissipated by Each Bulb
The power dissipated by each bulb can be calculated using the formula:
\[ P = I^2 R \]

#### For the 25 W bulb:
\[ P_{25} = I^2 \times R_{25} = (0.0909)^2 \times 1936 \approx 16.36 \, \text{W} \]

#### For the 100 W bulb:
\[ P_{100} = I^2 \times R_{100} = (0.0909)^2 \times 484 \approx 4.00 \, \text{W} \]

### Step 5: Compare the Power Dissipated
From the calculations:
- Power dissipated by the 25 W bulb \( \approx 16.36 \, \text{W} \)
- Power dissipated by the 100 W bulb \( \approx 4.00 \, \text{W} \)

### Conclusion
The 25 W bulb will glow brighter than the 100 W bulb when connected in series across a 220 V line.

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