If two bulbs of power 60 W and 100 W respectively each rated 110 V are connected in series with the supply of 220 V, then

Options

A. 60 W bulb will fuse
B. 100 W bulb will fuse
C. Both bulbs will fuse
D. Bubls will not fuse

Answer

To solve the problem step by step, we will analyze the two bulbs connected in series and determine which one will fuse when connected to a 220 V supply.

### Step 1: Calculate the resistance of each bulb

The power \( P \) of a bulb is given by the formula:
\[ P = \frac{V^2}{R} \]
Where \( V \) is the voltage rating of the bulb and \( R \) is the resistance.

#### For the 60 W bulb:
\[ R_1 = \frac{V^2}{P_1} = \frac{110^2}{60} = \frac{12100}{60} \approx 201.67 \, \Omega \]

#### For the 100 W bulb:
\[ R_2 = \frac{V^2}{P_2} = \frac{110^2}{100} = \frac{12100}{100} = 121 \, \Omega \]

### Step 2: Calculate the total resistance in the series circuit

Since the bulbs are connected in series, the total resistance \( R_{total} \) is the sum of the individual resistances:
\[ R_{total} = R_1 + R_2 = 201.67 + 121 = 322.67 \, \Omega \]

### Step 3: Calculate the current flowing through the circuit

Using Ohm's law, the current \( I \) can be calculated using the total voltage \( V_{supply} \) and the total resistance:
\[ I = \frac{V_{supply}}{R_{total}} = \frac{220}{322.67} \approx 0.68 \, A \]

### Step 4: Calculate the power consumed by each bulb

Now, we can calculate the power consumed by each bulb using the formula:
\[ P = I^2 R \]

#### Power consumed by the 60 W bulb:
\[ P_1 = I^2 R_1 = (0.68)^2 \times 201.67 \approx 93.78 \, W \]

#### Power consumed by the 100 W bulb:
\[ P_2 = I^2 R_2 = (0.68)^2 \times 121 \approx 56.27 \, W \]

### Step 5: Determine which bulb will fuse

Now we compare the power consumed by each bulb with their rated power:
- The 60 W bulb is consuming approximately 93.78 W, which is greater than its rated power of 60 W.
- The 100 W bulb is consuming approximately 56.27 W, which is less than its rated power of 100 W.

Since the 60 W bulb is consuming more power than it is rated for, it will fuse.

### Final Answer:
The 60 W bulb will fuse.

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