A factory is served by a 220 V supply line. In a circuit protected by a fuse marked 10 A, the maximum number of 100 W lamps in parallel that can be turned on, is

Options

A. 11
B. 22
C. 33
D. 66

Answer

To solve the problem of how many 100 W lamps can be turned on in parallel on a 220 V supply line with a fuse rated at 10 A, we can follow these steps:

### Step 1: Understand the power and voltage relationship
We know that the power (P) consumed by an electrical device is given by the formula:
\[ P = V \times I \]
where \( P \) is the power in watts, \( V \) is the voltage in volts, and \( I \) is the current in amperes.

### Step 2: Calculate the current drawn by one lamp
For a 100 W lamp connected to a 220 V supply, we can rearrange the formula to find the current \( I \):
\[ I = \frac{P}{V} \]
Substituting the values:
\[ I = \frac{100 \text{ W}}{220 \text{ V}} \]

### Step 3: Simplify the current calculation
Now, calculate the current:
\[ I = \frac{100}{220} = \frac{10}{22} \text{ A} \]
This simplifies to approximately:
\[ I \approx 0.4545 \text{ A} \]

### Step 4: Determine the total current for n lamps
If \( n \) lamps are connected in parallel, the total current \( I_{total} \) drawn from the supply will be:
\[ I_{total} = n \times I \]
Substituting the expression for \( I \):
\[ I_{total} = n \times \frac{10}{22} \]

### Step 5: Set up the inequality with the fuse rating
The total current must not exceed the fuse rating of 10 A:
\[ n \times \frac{10}{22} \leq 10 \]

### Step 6: Solve for n
To find the maximum number of lamps \( n \), we can rearrange the inequality:
\[ n \leq 10 \times \frac{22}{10} \]
\[ n \leq 22 \]

### Conclusion
Thus, the maximum number of 100 W lamps that can be turned on in parallel without exceeding the fuse rating is:
\[ n = 22 \]

### Final Answer
The maximum number of 100 W lamps that can be turned on is **22**.

---