If two bulbs of wattage 25 and 100 respectively each rated at 220 volt are connected in series with the supply of 440 volt , then which bulbs will fuse

Options

A. 100 watt bulb
B. 25 watt bulb
C. None of them
D. Both of them

Answer

To solve the problem of which bulb will fuse when a 25W and a 100W bulb are connected in series to a 440V supply, we can follow these steps:

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

**For the 25W bulb:**
- Rated Voltage, \( V = 220V \)
- Power, \( P = 25W \)

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

**For the 100W bulb:**
- Rated Voltage, \( V = 220V \)
- Power, \( P = 100W \)

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

### Step 2: Calculate the Total Resistance in Series
When resistors (bulbs) are connected in series, the total resistance \( R_{total} \) is the sum of the individual resistances:
\[ R_{total} = R_{25} + R_{100} \]
\[ R_{total} = 1936 + 484 = 2420 \, \Omega \]

### Step 3: Calculate the Current Flowing Through the Circuit
Using Ohm's Law, we can find the current \( I \) flowing through the circuit:
\[ I = \frac{V}{R_{total}} \]
where \( V = 440V \) (the supply voltage).

Calculating the current:
\[ I = \frac{440}{2420} \approx 0.1818 \, A \]

### Step 4: Calculate the Voltage Drop Across Each Bulb
In a series circuit, the voltage drop across each resistor can be calculated using:
\[ V = I \times R \]

**For the 25W bulb:**
\[ V_{25} = I \times R_{25} = 0.1818 \times 1936 \approx 352 \, V \]

**For the 100W bulb:**
\[ V_{100} = I \times R_{100} = 0.1818 \times 484 \approx 88 \, V \]

### Step 5: Determine Which Bulb Will Fuse
- The 25W bulb is rated for 220V but experiences a voltage drop of approximately 352V, which exceeds its rating. Therefore, the 25W bulb will fuse.
- The 100W bulb is rated for 220V but only experiences a voltage drop of approximately 88V, which is within its rating. Therefore, the 100W bulb will not fuse.

### Conclusion
The 25W bulb will fuse when connected in series with the 100W bulb to a 440V supply.

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