In a house 15 Bulbs of 45 W, 15 bulbs of 100 W, 15 bulbs of 10 W and Two heaters of 1 KW each is connected to 220 V Mains supply then find minimum fuse current

Options

A. 25 A
B. 15 A
C. `10 A`
D. 20 A

Answer

To find the minimum fuse current for the given electrical appliances in the house, we will follow these steps:

### Step 1: Calculate the current for each type of bulb and heater

1. **For 15 bulbs of 45 W:**
\[ I_1 = \frac{P_1}{V} = \frac{45 \, \text{W}}{220 \, \text{V}} = \frac{45}{220} \, \text{A} \]

2. **For 15 bulbs of 100 W:**
\[ I_2 = \frac{P_2}{V} = \frac{100 \, \text{W}}{220 \, \text{V}} = \frac{100}{220} \, \text{A} \]

3. **For 15 bulbs of 10 W:**
\[ I_3 = \frac{P_3}{V} = \frac{10 \, \text{W}}{220 \, \text{V}} = \frac{10}{220} \, \text{A} \]

4. **For 2 heaters of 1 kW each:**
\[ I_4 = \frac{P_4}{V} = \frac{1000 \, \text{W}}{220 \, \text{V}} = \frac{1000}{220} \, \text{A} \]

### Step 2: Calculate the total current for all appliances

Since all appliances are connected in parallel, the total current \( I \) can be calculated as follows:
\[ I = 15 I_1 + 15 I_2 + 15 I_3 + 2 I_4 \]

Substituting the values we calculated:
\[ I = 15 \left(\frac{45}{220}\right) + 15 \left(\frac{100}{220}\right) + 15 \left(\frac{10}{220}\right) + 2 \left(\frac{1000}{220}\right) \]

### Step 3: Simplify the expression

1. Factor out the common denominator:
\[ I = \frac{1}{220} \left( 15 \times 45 + 15 \times 100 + 15 \times 10 + 2 \times 1000 \right) \]

2. Calculate each term:
- \( 15 \times 45 = 675 \)
- \( 15 \times 100 = 1500 \)
- \( 15 \times 10 = 150 \)
- \( 2 \times 1000 = 2000 \)

3. Add these values together:
\[ I = \frac{1}{220} (675 + 1500 + 150 + 2000) = \frac{1}{220} (4325) \]

### Step 4: Calculate the total current

Now, calculate the total current:
\[ I = \frac{4325}{220} \approx 19.77 \, \text{A} \]

### Step 5: Determine the minimum fuse current

Since the fuse should be rated higher than the calculated current to avoid blowing during normal operation, we round up to the nearest standard fuse rating:
\[ \text{Minimum fuse current} \approx 20 \, \text{A} \]

### Final Answer:
The minimum fuse current required is **20 A**.

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