If two bulbs of 25 W and 100 W rated at 200 volts are connected in series across a 440 volts supply, then

Options

A. 100 watt bulb will fuse
B. 25 watt bulb will fuse
C. none of the bulb will fuse
D. both the bulbs will fuse

Explanation

To solve the problem step by step, let's analyze the situation where two bulbs rated at 25 W and 100 W (both rated for 200 V) are connected in series across a 440 V supply. We need to determine which bulb will fuse.

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

**For the 25 W bulb:**
\[ R_1 = \frac{200^2}{25} = \frac{40000}{25} = 1600 \, \Omega \]

**For the 100 W bulb:**
\[ R_2 = \frac{200^2}{100} = \frac{40000}{100} = 400 \, \Omega \]

### Step 2: Calculate Total Resistance in Series
When resistors are in series, the total resistance \( R_t \) is the sum of the individual resistances:
\[ R_t = R_1 + R_2 = 1600 \, \Omega + 400 \, \Omega = 2000 \, \Omega \]

### Step 3: Calculate the Current in the Circuit
Using Ohm's Law, we can find the current \( I \) flowing through the circuit when connected to a 440 V supply:
\[ I = \frac{V}{R_t} = \frac{440}{2000} = 0.22 \, \text{A} \]

### Step 4: Calculate the Power Dissipated by Each Bulb
Now, we can calculate the power dissipated by each bulb using the formula:
\[ P = I^2 R \]

**For the 25 W bulb:**
\[ P_1 = I^2 R_1 = (0.22)^2 \times 1600 = 0.0484 \times 1600 = 77.44 \, \text{W} \]

**For the 100 W bulb:**
\[ P_2 = I^2 R_2 = (0.22)^2 \times 400 = 0.0484 \times 400 = 19.36 \, \text{W} \]

### Step 5: Compare Dissipated Power with Rated Power
Now we compare the power dissipated by each bulb with their rated power:

- The 25 W bulb is dissipating 77.44 W, which exceeds its rated power of 25 W. Therefore, the 25 W bulb will fuse.
- The 100 W bulb is dissipating 19.36 W, which is less than its rated power of 100 W. Therefore, the 100 W bulb will not fuse.

### Conclusion
The 25 W bulb will fuse, while the 100 W bulb will not fuse.

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