Several electric bulbs designed to be used on a `220 V` electric supply line, are rated `10 W`. How many lamps can be connected in parallel with each other across the two wires of `220 V` line if the maximum allowable current is `5 A` ?

Options

A. 100
B. 200
C. 110
D. 120

Explanation

To solve the problem, we need to determine how many electric bulbs rated at 10 W can be connected in parallel across a 220 V supply line, given that the maximum allowable current is 5 A.

### Step-by-Step Solution:

1. **Understand the Power and Voltage Ratings**:
Each bulb is rated at 10 W and operates at a voltage of 220 V.

2. **Calculate the Resistance of Each Bulb**:
The resistance (R) of each bulb can be calculated using the formula:
\[ R = \frac{V^2}{P} \]
where \( V \) is the voltage (220 V) and \( P \) is the power (10 W).
\[ R = \frac{220^2}{10} = \frac{48400}{10} = 4840 \, \Omega \]

3. **Determine the Total Current**:
The maximum allowable current is given as 5 A.

4. **Set Up the Equation for Parallel Resistance**:
When bulbs are connected in parallel, the equivalent resistance \( R_{eq} \) can be expressed as:
\[ R_{eq} = \frac{R}{n} \]
where \( n \) is the number of bulbs.

5. **Apply Ohm's Law**:
According to Ohm's Law, the voltage across the equivalent resistance can be expressed as:
\[ V = I \times R_{eq} \]
Substituting the known values:
\[ 220 = 5 \times \frac{4840}{n} \]

6. **Rearranging the Equation**:
Rearranging the equation to solve for \( n \):
\[ n = 5 \times \frac{4840}{220} \]

7. **Calculating the Number of Bulbs**:
Simplifying the equation:
\[ n = \frac{5 \times 4840}{220} = \frac{24200}{220} = 110 \]

### Final Answer:
Thus, the maximum number of bulbs that can be connected in parallel is **110**.

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